Find the x and y Intercepts -2x^2+4x+16

$- 2 x^{2} + 4 x + 16$

Step 1

Write $- 2 x^{2} + 4 x + 16$ as an equation.

$y = - 2 x^{2} + 4 x + 16$

Step 2

Find the x-intercepts.

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

$0 = - 2 x^{2} + 4 x + 16$

Solve the equation.

Rewrite the equation as $- 2 x^{2} + 4 x + 16 = 0$ .

$- 2 x^{2} + 4 x + 16 = 0$

Factor the left side of the equation.

Factor $- 2$ out of $- 2 x^{2} + 4 x + 16$ .

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

$- 2 x^{2} + 4 x + 16 = 0$

Factor $- 2$ out of $4 x$ .

$- 2 x^{2} - 2 (- 2 x) + 16 = 0$

Factor $- 2$ out of $16$ .

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

Factor $- 2$ out of $- 2 (x^{2}) - 2 (- 2 x)$ .

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

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

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

Factor.

Factor $x^{2} - 2 x - 8$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 8$ and whose sum is $- 2$ .

$- 4, 2$

Write the factored form using these integers.

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

Remove unnecessary parentheses.

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

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

$x - 4 = 0$

$x + 2 = 0$

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

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

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

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

$x = 4, - 2$

x-intercept(s) in point form.

x-intercept(s): $(4, 0), (- 2, 0)$

Step 3

Find the y-intercepts.

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

$y = - 2 {(0)}^{2} + 4 (0) + 16$

Solve the equation.

Remove parentheses.

$y = - 2 \cdot 0^{2} + 4 (0) + 16$

Remove parentheses.

$y = - 2 {(0)}^{2} + 4 (0) + 16$

Simplify $- 2 {(0)}^{2} + 4 (0) + 16$ .

Simplify each term.

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

$y = - 2 \cdot 0 + 4 (0) + 16$

Multiply $- 2$ by $0$ .

$y = 0 + 4 (0) + 16$

Multiply $4$ by $0$ .

$y = 0 + 0 + 16$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 16$

Add $0$ and $16$ .

$y = 16$

y-intercept(s) in point form.

y-intercept(s): $(0, 16)$

Step 4

List the intersections.

x-intercept(s): $(4, 0), (- 2, 0)$

y-intercept(s): $(0, 16)$

Step 5

Find the x and y Intercepts -2x^2+4x+16

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