Find the x and y Intercepts -(x+3)^2+16

$- {(x + 3)}^{2} + 16$

Step 1

Write $- {(x + 3)}^{2} + 16$ as an equation.

$y = - {(x + 3)}^{2} + 16$

Step 2

Find the x-intercepts.

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

$0 = - {(x + 3)}^{2} + 16$

Solve the equation.

Remove parentheses.

$0 = - {(x + 3)}^{2} + 16$

Simplify $- {(x + 3)}^{2} + 16$ .

Simplify each term.

Rewrite ${(x + 3)}^{2}$ as $(x + 3) (x + 3)$ .

$0 = - ((x + 3) (x + 3)) + 16$

Expand $(x + 3) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$0 = - (x (x + 3) + 3 (x + 3)) + 16$

Apply the distributive property.

$0 = - (x \cdot x + x \cdot 3 + 3 (x + 3)) + 16$

Apply the distributive property.

$0 = - (x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3) + 16$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$0 = - (x^{2} + x \cdot 3 + 3 x + 3 \cdot 3) + 16$

Move $3$ to the left of $x$ .

$0 = - (x^{2} + 3 \cdot x + 3 x + 3 \cdot 3) + 16$

Multiply $3$ by $3$ .

$0 = - (x^{2} + 3 x + 3 x + 9) + 16$

Add $3 x$ and $3 x$ .

$0 = - (x^{2} + 6 x + 9) + 16$

Apply the distributive property.

$0 = - x^{2} - (6 x) - 1 \cdot 9 + 16$

Simplify.

Multiply $6$ by $- 1$ .

$0 = - x^{2} - 6 x - 1 \cdot 9 + 16$

Multiply $- 1$ by $9$ .

$0 = - x^{2} - 6 x - 9 + 16$

Add $- 9$ and $16$ .

$0 = - x^{2} - 6 x + 7$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = - 7, 1$

x-intercept(s) in point form.

x-intercept(s): $(- 7, 0), (1, 0)$

Step 3

Find the y-intercepts.

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

$y = - {((0) + 3)}^{2} + 16$

Solve the equation.

Remove parentheses.

$y = - {(0 + 3)}^{2} + 16$

Remove parentheses.

$y = - {((0) + 3)}^{2} + 16$

Simplify $- {((0) + 3)}^{2} + 16$ .

Simplify each term.

Add $0$ and $3$ .

$y = - 3^{2} + 16$

Raise $3$ to the power of $2$ .

$y = - 1 \cdot 9 + 16$

Multiply $- 1$ by $9$ .

$y = - 9 + 16$

Add $- 9$ and $16$ .

$y = 7$

y-intercept(s) in point form.

y-intercept(s): $(0, 7)$

Step 4

List the intersections.

x-intercept(s): $(- 7, 0), (1, 0)$

y-intercept(s): $(0, 7)$

Step 5

Find the x and y Intercepts -(x+3)^2+16

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