Algebra Examples

$(- 6, 2)$ , $(- 5, 2.75)$ , $(- 4, 2.5)$

Step 1

Use the standard form of a quadratic equation $y = a x^{2} + b x + c$ as the starting point for finding the equation through the three points.

$y = a x^{2} + b x + c$

Step 2

Create a system of equations by substituting the $x$ and $y$ values of each point into the standard formula of a quadratic equation to create the three equation system.

$2 = a {(- 6)}^{2} + b (- 6) + c, 2.75 = a {(- 5)}^{2} + b (- 5) + c, 2.5 = a {(- 4)}^{2} + b (- 4) + c$

Step 3

Solve the system of equations to find the values of $a$ , $b$ , and $c$ .

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Step 3.1

Solve for $c$ in $2 = a {(- 6)}^{2} + b (- 6) + c$ .

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Step 3.1.1

Rewrite the equation as $a {(- 6)}^{2} + b (- 6) + c = 2$ .

$a {(- 6)}^{2} + b (- 6) + c = 2$

$2.75 = a {(- 5)}^{2} + b (- 5) + c$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

Step 3.1.2

Simplify each term.

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Step 3.1.2.1

Raise $- 6$ to the power of $2$ .

$a \cdot 36 + b (- 6) + c = 2$

$2.75 = a {(- 5)}^{2} + b (- 5) + c$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

Step 3.1.2.2

Move $36$ to the left of $a$ .

$36 \cdot a + b (- 6) + c = 2$

$2.75 = a {(- 5)}^{2} + b (- 5) + c$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

Step 3.1.2.3

Move $- 6$ to the left of $b$ .

$36 a - 6 b + c = 2$

$2.75 = a {(- 5)}^{2} + b (- 5) + c$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

$36 a - 6 b + c = 2$

$2.75 = a {(- 5)}^{2} + b (- 5) + c$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

Step 3.1.3

Move all terms not containing $c$ to the right side of the equation.

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Step 3.1.3.1

Subtract $36 a$ from both sides of the equation.

$- 6 b + c = 2 - 36 a$

$2.75 = a {(- 5)}^{2} + b (- 5) + c$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

Step 3.1.3.2

Add $6 b$ to both sides of the equation.

$c = 2 - 36 a + 6 b$

$2.75 = a {(- 5)}^{2} + b (- 5) + c$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

$c = 2 - 36 a + 6 b$

$2.75 = a {(- 5)}^{2} + b (- 5) + c$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

$c = 2 - 36 a + 6 b$

$2.75 = a {(- 5)}^{2} + b (- 5) + c$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

Step 3.2

Replace all occurrences of $c$ with $2 - 36 a + 6 b$ in each equation.

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Step 3.2.1

Replace all occurrences of $c$ in $2.75 = a {(- 5)}^{2} + b (- 5) + c$ with $2 - 36 a + 6 b$ .

$2.75 = a {(- 5)}^{2} + b (- 5) + 2 - 36 a + 6 b$

$c = 2 - 36 a + 6 b$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

Step 3.2.2

Simplify $2.75 = a {(- 5)}^{2} + b (- 5) + 2 - 36 a + 6 b$ .

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Step 3.2.2.1

Simplify the left side.

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Step 3.2.2.1.1

Remove parentheses.

$2.75 = a {(- 5)}^{2} + b (- 5) + 2 - 36 a + 6 b$

$c = 2 - 36 a + 6 b$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

$2.75 = a {(- 5)}^{2} + b (- 5) + 2 - 36 a + 6 b$

$c = 2 - 36 a + 6 b$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

Step 3.2.2.2

Simplify the right side.

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Step 3.2.2.2.1

Simplify $a {(- 5)}^{2} + b (- 5) + 2 - 36 a + 6 b$ .

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Step 3.2.2.2.1.1

Simplify each term.

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Step 3.2.2.2.1.1.1

Raise $- 5$ to the power of $2$ .

$2.75 = a \cdot 25 + b (- 5) + 2 - 36 a + 6 b$

$c = 2 - 36 a + 6 b$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

Step 3.2.2.2.1.1.2

Move $25$ to the left of $a$ .

$2.75 = 25 \cdot a + b (- 5) + 2 - 36 a + 6 b$

$c = 2 - 36 a + 6 b$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

Step 3.2.2.2.1.1.3

Move $- 5$ to the left of $b$ .

$2.75 = 25 a - 5 b + 2 - 36 a + 6 b$

$c = 2 - 36 a + 6 b$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

$2.75 = 25 a - 5 b + 2 - 36 a + 6 b$

$c = 2 - 36 a + 6 b$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

Step 3.2.2.2.1.2

Simplify by adding terms.

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Step 3.2.2.2.1.2.1

Subtract $36 a$ from $25 a$ .

$2.75 = - 11 a - 5 b + 2 + 6 b$

$c = 2 - 36 a + 6 b$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

Step 3.2.2.2.1.2.2

Add $- 5 b$ and $6 b$ .

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

$2.5 = a {(- 4)}^{2} + b (- 4) + c$

Step 3.2.3

Replace all occurrences of $c$ in $2.5 = a {(- 4)}^{2} + b (- 4) + c$ with $2 - 36 a + 6 b$ .

$2.5 = a {(- 4)}^{2} + b (- 4) + 2 - 36 a + 6 b$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

Step 3.2.4

Simplify $2.5 = a {(- 4)}^{2} + b (- 4) + 2 - 36 a + 6 b$ .

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Step 3.2.4.1

Simplify the left side.

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Step 3.2.4.1.1

Remove parentheses.

$2.5 = a {(- 4)}^{2} + b (- 4) + 2 - 36 a + 6 b$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

$2.5 = a {(- 4)}^{2} + b (- 4) + 2 - 36 a + 6 b$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

Step 3.2.4.2

Simplify the right side.

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Step 3.2.4.2.1

Simplify $a {(- 4)}^{2} + b (- 4) + 2 - 36 a + 6 b$ .

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Step 3.2.4.2.1.1

Simplify each term.

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Step 3.2.4.2.1.1.1

Raise $- 4$ to the power of $2$ .

$2.5 = a \cdot 16 + b (- 4) + 2 - 36 a + 6 b$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

Step 3.2.4.2.1.1.2

Move $16$ to the left of $a$ .

$2.5 = 16 \cdot a + b (- 4) + 2 - 36 a + 6 b$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

Step 3.2.4.2.1.1.3

Move $- 4$ to the left of $b$ .

$2.5 = 16 a - 4 b + 2 - 36 a + 6 b$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

$2.5 = 16 a - 4 b + 2 - 36 a + 6 b$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

Step 3.2.4.2.1.2

Simplify by adding terms.

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Step 3.2.4.2.1.2.1

Subtract $36 a$ from $16 a$ .

$2.5 = - 20 a - 4 b + 2 + 6 b$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

Step 3.2.4.2.1.2.2

Add $- 4 b$ and $6 b$ .

$2.5 = - 20 a + 2 b + 2$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

$2.5 = - 20 a + 2 b + 2$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

$2.5 = - 20 a + 2 b + 2$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

$2.5 = - 20 a + 2 b + 2$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

$2.5 = - 20 a + 2 b + 2$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

$2.5 = - 20 a + 2 b + 2$

$2.75 = - 11 a + b + 2$

$c = 2 - 36 a + 6 b$

Step 3.3

Solve for $b$ in $2.75 = - 11 a + b + 2$ .

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Step 3.3.1

Rewrite the equation as $- 11 a + b + 2 = 2.75$ .

$- 11 a + b + 2 = 2.75$

$2.5 = - 20 a + 2 b + 2$

$c = 2 - 36 a + 6 b$

Step 3.3.2

Move all terms not containing $b$ to the right side of the equation.

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Step 3.3.2.1

Add $11 a$ to both sides of the equation.

$b + 2 = 2.75 + 11 a$

$2.5 = - 20 a + 2 b + 2$

$c = 2 - 36 a + 6 b$

Step 3.3.2.2

Subtract $2$ from both sides of the equation.

$b = 2.75 + 11 a - 2$

$2.5 = - 20 a + 2 b + 2$

$c = 2 - 36 a + 6 b$

Step 3.3.2.3

Subtract $2$ from $2.75$ .

$b = 11 a + 0.75$

$2.5 = - 20 a + 2 b + 2$

$c = 2 - 36 a + 6 b$

$b = 11 a + 0.75$

$2.5 = - 20 a + 2 b + 2$

$c = 2 - 36 a + 6 b$

$b = 11 a + 0.75$

$2.5 = - 20 a + 2 b + 2$

$c = 2 - 36 a + 6 b$

Step 3.4

Replace all occurrences of $b$ with $11 a + 0.75$ in each equation.

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Step 3.4.1

Replace all occurrences of $b$ in $2.5 = - 20 a + 2 b + 2$ with $11 a + 0.75$ .

$2.5 = - 20 a + 2 (11 a + 0.75) + 2$

$b = 11 a + 0.75$

$c = 2 - 36 a + 6 b$

Step 3.4.2

Simplify the right side.

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Step 3.4.2.1

Simplify $- 20 a + 2 (11 a + 0.75) + 2$ .

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Step 3.4.2.1.1

Simplify each term.

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Step 3.4.2.1.1.1

Apply the distributive property.

$2.5 = - 20 a + 2 (11 a) + 2 \cdot 0.75 + 2$

$b = 11 a + 0.75$

$c = 2 - 36 a + 6 b$

Step 3.4.2.1.1.2

Multiply $11$ by $2$ .

$2.5 = - 20 a + 22 a + 2 \cdot 0.75 + 2$

$b = 11 a + 0.75$

$c = 2 - 36 a + 6 b$

Step 3.4.2.1.1.3

Multiply $2$ by $0.75$ .

$2.5 = - 20 a + 22 a + 1.5 + 2$

$b = 11 a + 0.75$

$c = 2 - 36 a + 6 b$

$2.5 = - 20 a + 22 a + 1.5 + 2$

$b = 11 a + 0.75$

$c = 2 - 36 a + 6 b$

Step 3.4.2.1.2

Simplify by adding terms.

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Step 3.4.2.1.2.1

Add $- 20 a$ and $22 a$ .

$2.5 = 2 a + 1.5 + 2$

$b = 11 a + 0.75$

$c = 2 - 36 a + 6 b$

Step 3.4.2.1.2.2

Add $1.5$ and $2$ .

$2.5 = 2 a + 3.5$

$b = 11 a + 0.75$

$c = 2 - 36 a + 6 b$

$2.5 = 2 a + 3.5$

$b = 11 a + 0.75$

$c = 2 - 36 a + 6 b$

$2.5 = 2 a + 3.5$

$b = 11 a + 0.75$

$c = 2 - 36 a + 6 b$

$2.5 = 2 a + 3.5$

$b = 11 a + 0.75$

$c = 2 - 36 a + 6 b$

Step 3.4.3

Replace all occurrences of $b$ in $c = 2 - 36 a + 6 b$ with $11 a + 0.75$ .

$c = 2 - 36 a + 6 (11 a + 0.75)$

$2.5 = 2 a + 3.5$

$b = 11 a + 0.75$

Step 3.4.4

Simplify the right side.

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Step 3.4.4.1

Simplify $2 - 36 a + 6 (11 a + 0.75)$ .

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Step 3.4.4.1.1

Simplify each term.

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Step 3.4.4.1.1.1

Apply the distributive property.

$c = 2 - 36 a + 6 (11 a) + 6 \cdot 0.75$

$2.5 = 2 a + 3.5$

$b = 11 a + 0.75$

Step 3.4.4.1.1.2

Multiply $11$ by $6$ .

$c = 2 - 36 a + 66 a + 6 \cdot 0.75$

$2.5 = 2 a + 3.5$

$b = 11 a + 0.75$

Step 3.4.4.1.1.3

Multiply $6$ by $0.75$ .

$c = 2 - 36 a + 66 a + 4.5$

$2.5 = 2 a + 3.5$

$b = 11 a + 0.75$

$c = 2 - 36 a + 66 a + 4.5$

$2.5 = 2 a + 3.5$

$b = 11 a + 0.75$

Step 3.4.4.1.2

Simplify by adding terms.

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Step 3.4.4.1.2.1

Add $2$ and $4.5$ .

$c = - 36 a + 66 a + 6.5$

$2.5 = 2 a + 3.5$

$b = 11 a + 0.75$

Step 3.4.4.1.2.2

Add $- 36 a$ and $66 a$ .

$c = 30 a + 6.5$

$2.5 = 2 a + 3.5$

$b = 11 a + 0.75$

$c = 30 a + 6.5$

$2.5 = 2 a + 3.5$

$b = 11 a + 0.75$

$c = 30 a + 6.5$

$2.5 = 2 a + 3.5$

$b = 11 a + 0.75$

$c = 30 a + 6.5$

$2.5 = 2 a + 3.5$

$b = 11 a + 0.75$

$c = 30 a + 6.5$

$2.5 = 2 a + 3.5$

$b = 11 a + 0.75$

Step 3.5

Solve for $a$ in $2.5 = 2 a + 3.5$ .

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Step 3.5.1

Rewrite the equation as $2 a + 3.5 = 2.5$ .

$2 a + 3.5 = 2.5$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

Step 3.5.2

Move all terms not containing $a$ to the right side of the equation.

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Step 3.5.2.1

Subtract $3.5$ from both sides of the equation.

$2 a = 2.5 - 3.5$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

Step 3.5.2.2

Subtract $3.5$ from $2.5$ .

$2 a = - 1$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

$2 a = - 1$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

Step 3.5.3

Divide each term in $2 a = - 1$ by $2$ and simplify.

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Step 3.5.3.1

Divide each term in $2 a = - 1$ by $2$ .

$\frac{2 a}{2} = \frac{- 1}{2}$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

Step 3.5.3.2

Simplify the left side.

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Step 3.5.3.2.1

Cancel the common factor of $2$ .

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Step 3.5.3.2.1.1

Cancel the common factor.

$\frac{2 a}{2} = \frac{- 1}{2}$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

Step 3.5.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 1}{2}$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

$a = \frac{- 1}{2}$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

$a = \frac{- 1}{2}$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

Step 3.5.3.3

Simplify the right side.

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Step 3.5.3.3.1

Cancel the common factor of $- 1$ and $2$ .

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Step 3.5.3.3.1.1

Rewrite $- 1$ as $1 (- 1)$ .

$a = \frac{1 (- 1)}{2}$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

Step 3.5.3.3.1.2

Cancel the common factors.

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Step 3.5.3.3.1.2.1

Rewrite $2$ as $1 (2)$ .

$a = \frac{1 \cdot - 1}{1 \cdot 2}$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

Step 3.5.3.3.1.2.2

Cancel the common factor.

$a = \frac{1 \cdot - 1}{1 \cdot 2}$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

Step 3.5.3.3.1.2.3

Rewrite the expression.

$a = \frac{- 1}{2}$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

$a = \frac{- 1}{2}$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

$a = \frac{- 1}{2}$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

Step 3.5.3.3.2

Move the negative in front of the fraction.

$a = - \frac{1}{2}$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

$a = - \frac{1}{2}$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

$a = - \frac{1}{2}$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

$a = - \frac{1}{2}$

$c = 30 a + 6.5$

$b = 11 a + 0.75$

Step 3.6

Replace all occurrences of $a$ with $- \frac{1}{2}$ in each equation.

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Step 3.6.1

Replace all occurrences of $a$ in $c = 30 a + 6.5$ with $- \frac{1}{2}$ .

$c = 30 (- \frac{1}{2}) + 6.5$

$a = - \frac{1}{2}$

$b = 11 a + 0.75$

Step 3.6.2

Simplify the right side.

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Step 3.6.2.1

Simplify $30 (- \frac{1}{2}) + 6.5$ .

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Step 3.6.2.1.1

Simplify each term.

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Step 3.6.2.1.1.1

Cancel the common factor of $2$ .

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Step 3.6.2.1.1.1.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$c = 30 (\frac{- 1}{2}) + 6.5$

$a = - \frac{1}{2}$

$b = 11 a + 0.75$

Step 3.6.2.1.1.1.2

Factor $2$ out of $30$ .

$c = 2 (15) (\frac{- 1}{2}) + 6.5$

$a = - \frac{1}{2}$

$b = 11 a + 0.75$

Step 3.6.2.1.1.1.3

Cancel the common factor.

$c = 2 \cdot (15 (\frac{- 1}{2})) + 6.5$

$a = - \frac{1}{2}$

$b = 11 a + 0.75$

Step 3.6.2.1.1.1.4

Rewrite the expression.

$c = 15 \cdot - 1 + 6.5$

$a = - \frac{1}{2}$

$b = 11 a + 0.75$

$c = 15 \cdot - 1 + 6.5$

$a = - \frac{1}{2}$

$b = 11 a + 0.75$

Step 3.6.2.1.1.2

Multiply $15$ by $- 1$ .

$c = - 15 + 6.5$

$a = - \frac{1}{2}$

$b = 11 a + 0.75$

$c = - 15 + 6.5$

$a = - \frac{1}{2}$

$b = 11 a + 0.75$

Step 3.6.2.1.2

Add $- 15$ and $6.5$ .

$c = - 8.5$

$a = - \frac{1}{2}$

$b = 11 a + 0.75$

$c = - 8.5$

$a = - \frac{1}{2}$

$b = 11 a + 0.75$

$c = - 8.5$

$a = - \frac{1}{2}$

$b = 11 a + 0.75$

Step 3.6.3

Replace all occurrences of $a$ in $b = 11 a + 0.75$ with $- \frac{1}{2}$ .

$b = 11 (- \frac{1}{2}) + 0.75$

$c = - 8.5$

$a = - \frac{1}{2}$

Step 3.6.4

Simplify the right side.

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Step 3.6.4.1

Simplify $11 (- \frac{1}{2}) + 0.75$ .

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Step 3.6.4.1.1

Simplify each term.

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Step 3.6.4.1.1.1

Multiply $11 (- \frac{1}{2})$ .

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Step 3.6.4.1.1.1.1

Multiply $- 1$ by $11$ .

$b = - 11 (\frac{1}{2}) + 0.75$

$c = - 8.5$

$a = - \frac{1}{2}$

Step 3.6.4.1.1.1.2

Combine $- 11$ and $\frac{1}{2}$ .

$b = \frac{- 11}{2} + 0.75$

$c = - 8.5$

$a = - \frac{1}{2}$

$b = \frac{- 11}{2} + 0.75$

$c = - 8.5$

$a = - \frac{1}{2}$

Step 3.6.4.1.1.2

Move the negative in front of the fraction.

$b = - \frac{11}{2} + 0.75$

$c = - 8.5$

$a = - \frac{1}{2}$

$b = - \frac{11}{2} + 0.75$

$c = - 8.5$

$a = - \frac{1}{2}$

Step 3.6.4.1.2

To write $0.75$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b = - \frac{11}{2} + 0.75 \cdot \frac{2}{2}$

$c = - 8.5$

$a = - \frac{1}{2}$

Step 3.6.4.1.3

Combine fractions.

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Step 3.6.4.1.3.1

Combine $0.75$ and $\frac{2}{2}$ .

$b = - \frac{11}{2} + \frac{0.75 \cdot 2}{2}$

$c = - 8.5$

$a = - \frac{1}{2}$

Step 3.6.4.1.3.2

Combine the numerators over the common denominator.

$b = \frac{- 11 + 0.75 \cdot 2}{2}$

$c = - 8.5$

$a = - \frac{1}{2}$

$b = \frac{- 11 + 0.75 \cdot 2}{2}$

$c = - 8.5$

$a = - \frac{1}{2}$

Step 3.6.4.1.4

Simplify the numerator.

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Step 3.6.4.1.4.1

Multiply $0.75$ by $2$ .

$b = \frac{- 11 + 1.5}{2}$

$c = - 8.5$

$a = - \frac{1}{2}$

Step 3.6.4.1.4.2

Add $- 11$ and $1.5$ .

$b = \frac{- 9.5}{2}$

$c = - 8.5$

$a = - \frac{1}{2}$

$b = \frac{- 9.5}{2}$

$c = - 8.5$

$a = - \frac{1}{2}$

Step 3.6.4.1.5

Divide $- 9.5$ by $2$ .

$b = - 4.75$

$c = - 8.5$

$a = - \frac{1}{2}$

$b = - 4.75$

$c = - 8.5$

$a = - \frac{1}{2}$

$b = - 4.75$

$c = - 8.5$

$a = - \frac{1}{2}$

$b = - 4.75$

$c = - 8.5$

$a = - \frac{1}{2}$

Step 3.7

List all of the solutions.

$b = - 4.75, c = - 8.5, a = - \frac{1}{2}$

Step 4

Substitute the actual values of $a$ , $b$ , and $c$ into the formula for a quadratic equation to find the resulting equation.

$y = - \frac{x^{2}}{2} - 4.75 x - 8.5$

Step 5