Precalculus Examples

$f (x) = 2 x^{2} - 8 x$

Step 1

Find the x-intercepts.

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

$0 = 2 x^{2} - 8 x$

Solve the equation.

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Rewrite the equation as $2 x^{2} - 8 x = 0$ .

$2 x^{2} - 8 x = 0$

Factor $2 x$ out of $2 x^{2} - 8 x$ .

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Factor $2 x$ out of $2 x^{2}$ .

$2 x (x) - 8 x = 0$

Factor $2 x$ out of $- 8 x$ .

$2 x (x) + 2 x (- 4) = 0$

Factor $2 x$ out of $2 x (x) + 2 x (- 4)$ .

$2 x (x - 4) = 0$

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

$x = 0$

$x - 4 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 4$ equal to $0$ and solve for $x$ .

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Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

The final solution is all the values that make $2 x (x - 4) = 0$ true.

$x = 0, 4$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (4, 0)$

Step 2

Find the y-intercepts.

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

$y = 2 {(0)}^{2} - 8 \cdot 0$

Solve the equation.

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Remove parentheses.

$y = 2 \cdot 0^{2} - 8 \cdot 0$

Remove parentheses.

$y = 2 {(0)}^{2} - 8 \cdot 0$

Simplify $2 {(0)}^{2} - 8 \cdot 0$ .

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Simplify each term.

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

$y = 2 \cdot 0 - 8 \cdot 0$

Multiply $2$ by $0$ .

$y = 0 - 8 \cdot 0$

Multiply $- 8$ by $0$ .

$y = 0 + 0$

Add $0$ and $0$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(0, 0), (4, 0)$

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

Step 4