Algebra Examples

$(x - 1) (- x + 5) = y$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$(x - 1) (- x + 5) = 0$

Step 1.2

Solve the equation.

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Step 1.2.1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 1 = 0$

$- x + 5 = 0$

Step 1.2.2

Set $x - 1$ equal to $0$ and solve for $x$ .

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Step 1.2.2.1

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Step 1.2.2.2

Add $1$ to both sides of the equation.

$x = 1$

Step 1.2.3

Set $- x + 5$ equal to $0$ and solve for $x$ .

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Step 1.2.3.1

Set $- x + 5$ equal to $0$ .

$- x + 5 = 0$

Step 1.2.3.2

Solve $- x + 5 = 0$ for $x$ .

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Step 1.2.3.2.1

Subtract $5$ from both sides of the equation.

$- x = - 5$

Step 1.2.3.2.2

Divide each term in $- x = - 5$ by $- 1$ and simplify.

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Step 1.2.3.2.2.1

Divide each term in $- x = - 5$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 5}{- 1}$

Step 1.2.3.2.2.2

Simplify the left side.

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Step 1.2.3.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 5}{- 1}$

Step 1.2.3.2.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 5}{- 1}$

Step 1.2.3.2.2.3

Simplify the right side.

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Step 1.2.3.2.2.3.1

Divide $- 5$ by $- 1$ .

$x = 5$

Step 1.2.4

The final solution is all the values that make $(x - 1) (- x + 5) = 0$ true.

$x = 1, 5$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(1, 0), (5, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$((0) - 1) (- (0) + 5) = y$

Step 2.2

Solve the equation.

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Step 2.2.1

Rewrite the equation as $y = ((0) - 1) (- (0) + 5)$ .

$y = ((0) - 1) (- (0) + 5)$

Step 2.2.2

Simplify $((0) - 1) (- (0) + 5)$ .

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Step 2.2.2.1

Subtract $1$ from $0$ .

$y = - 1 (- (0) + 5)$

Step 2.2.2.2

Multiply $- 1$ by $0$ .

$y = - 1 (0 + 5)$

Step 2.2.2.3

Add $0$ and $5$ .

$y = - 1 \cdot 5$

Step 2.2.2.4

Multiply $- 1$ by $5$ .

$y = - 5$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 5)$

Step 3

List the intersections.

x-intercept(s): $(1, 0), (5, 0)$

y-intercept(s): $(0, - 5)$

Step 4