Algebra Examples

$(0, - 25)$ , $(0, 25)$ , $(0, 24)$

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.

$- 25 = a {(0)}^{2} + b (0) + c, 25 = a {(0)}^{2} + b (0) + c, 24 = a {(0)}^{2} + b (0) + c$

Step 3

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

Tap for more steps...

Step 3.1

Solve for $c$ in $- 25 = a \cdot 0^{2} + c$ .

Tap for more steps...

Step 3.1.1

Rewrite the equation as $a \cdot 0^{2} + c = - 25$ .

$a \cdot 0^{2} + c = - 25$

$25 = a \cdot 0^{2} + c$

$24 = a \cdot 0^{2} + c$

Step 3.1.2

Simplify $a \cdot 0^{2} + c$ .

Tap for more steps...

Step 3.1.2.1

Simplify each term.

Tap for more steps...

Step 3.1.2.1.1

Raising $0$ to any positive power yields $0$ .

$a \cdot 0 + c = - 25$

$25 = a \cdot 0^{2} + c$

$24 = a \cdot 0^{2} + c$

Step 3.1.2.1.2

Multiply $a$ by $0$ .

$0 + c = - 25$

$25 = a \cdot 0^{2} + c$

$24 = a \cdot 0^{2} + c$

$0 + c = - 25$

$25 = a \cdot 0^{2} + c$

$24 = a \cdot 0^{2} + c$

Step 3.1.2.2

Add $0$ and $c$ .

$c = - 25$

$25 = a \cdot 0^{2} + c$

$24 = a \cdot 0^{2} + c$

$c = - 25$

$25 = a \cdot 0^{2} + c$

$24 = a \cdot 0^{2} + c$

$c = - 25$

$25 = a \cdot 0^{2} + c$

$24 = a \cdot 0^{2} + c$

Step 3.2

Replace all occurrences of $c$ with $- 25$ in each equation.

Tap for more steps...

Step 3.2.1

Replace all occurrences of $c$ in $25 = a \cdot 0^{2} + c$ with $- 25$ .

$25 = a \cdot 0^{2} - 25$

$c = - 25$

$24 = a \cdot 0^{2} + c$

Step 3.2.2

Simplify $25 = a \cdot 0^{2} - 25$ .

Tap for more steps...

Step 3.2.2.1

Simplify the left side.

Tap for more steps...

Step 3.2.2.1.1

Remove parentheses.

$25 = a \cdot 0^{2} - 25$

$c = - 25$

$24 = a \cdot 0^{2} + c$

$25 = a \cdot 0^{2} - 25$

$c = - 25$

$24 = a \cdot 0^{2} + c$

Step 3.2.2.2

Simplify the right side.

Tap for more steps...

Step 3.2.2.2.1

Simplify $a \cdot 0^{2} - 25$ .

Tap for more steps...

Step 3.2.2.2.1.1

Simplify each term.

Tap for more steps...

Step 3.2.2.2.1.1.1

Raising $0$ to any positive power yields $0$ .

$25 = a \cdot 0 - 25$

$c = - 25$

$24 = a \cdot 0^{2} + c$

Step 3.2.2.2.1.1.2

Multiply $a$ by $0$ .

$25 = 0 - 25$

$c = - 25$

$24 = a \cdot 0^{2} + c$

$25 = 0 - 25$

$c = - 25$

$24 = a \cdot 0^{2} + c$

Step 3.2.2.2.1.2

Subtract $25$ from $0$ .

$25 = - 25$

$c = - 25$

$24 = a \cdot 0^{2} + c$

$25 = - 25$

$c = - 25$

$24 = a \cdot 0^{2} + c$

$25 = - 25$

$c = - 25$

$24 = a \cdot 0^{2} + c$

$25 = - 25$

$c = - 25$

$24 = a \cdot 0^{2} + c$

Step 3.2.3

Replace all occurrences of $c$ in $24 = a \cdot 0^{2} + c$ with $- 25$ .

$24 = a \cdot 0^{2} - 25$

$25 = - 25$

$c = - 25$

Step 3.2.4

Simplify $24 = a \cdot 0^{2} - 25$ .

Tap for more steps...

Step 3.2.4.1

Simplify the left side.

Tap for more steps...

Step 3.2.4.1.1

Remove parentheses.

$24 = a \cdot 0^{2} - 25$

$25 = - 25$

$c = - 25$

$24 = a \cdot 0^{2} - 25$

$25 = - 25$

$c = - 25$

Step 3.2.4.2

Simplify the right side.

Tap for more steps...

Step 3.2.4.2.1

Simplify $a \cdot 0^{2} - 25$ .

Tap for more steps...

Step 3.2.4.2.1.1

Simplify each term.

Tap for more steps...

Step 3.2.4.2.1.1.1

Raising $0$ to any positive power yields $0$ .

$24 = a \cdot 0 - 25$

$25 = - 25$

$c = - 25$

Step 3.2.4.2.1.1.2

Multiply $a$ by $0$ .

$24 = 0 - 25$

$25 = - 25$

$c = - 25$

$24 = 0 - 25$

$25 = - 25$

$c = - 25$

Step 3.2.4.2.1.2

Subtract $25$ from $0$ .

$24 = - 25$

$25 = - 25$

$c = - 25$

$24 = - 25$

$25 = - 25$

$c = - 25$

$24 = - 25$

$25 = - 25$

$c = - 25$

$24 = - 25$

$25 = - 25$

$c = - 25$

$24 = - 25$

$25 = - 25$

$c = - 25$

Step 3.3

Since $24 = - 25$ is not true, there is no solution.

No solution