Find the X and Y Intercepts -2(x-5)^2+2

$- 2 {(x - 5)}^{2} + 2$

Write $- 2 {(x - 5)}^{2} + 2$ as an equation.

$y = - 2 {(x - 5)}^{2} + 2$

Find the x-intercepts.

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

$0 = - 2 {(x - 5)}^{2} + 2$

Solve the equation.

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Remove parentheses.

$0 = - 2 {(x - 5)}^{2} + 2$

Simplify $- 2 {(x - 5)}^{2} + 2$ .

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Simplify each term.

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Rewrite ${(x - 5)}^{2}$ as $(x - 5) (x - 5)$ .

$0 = - 2 ((x - 5) (x - 5)) + 2$

Expand $(x - 5) (x - 5)$ using the FOIL Method.

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Apply the distributive property.

$0 = - 2 (x (x - 5) - 5 (x - 5)) + 2$

Apply the distributive property.

$0 = - 2 (x \cdot x + x \cdot - 5 - 5 (x - 5)) + 2$

Apply the distributive property.

$0 = - 2 (x \cdot x + x \cdot - 5 - 5 x - 5 \cdot - 5) + 2$

Simplify and combine like terms.

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Simplify each term.

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Multiply $x$ by $x$ .

$0 = - 2 (x^{2} + x \cdot - 5 - 5 x - 5 \cdot - 5) + 2$

Move $- 5$ to the left of $x$ .

$0 = - 2 (x^{2} - 5 \cdot x - 5 x - 5 \cdot - 5) + 2$

Multiply $- 5$ by $- 5$ .

$0 = - 2 (x^{2} - 5 x - 5 x + 25) + 2$

Subtract $5 x$ from $- 5 x$ .

$0 = - 2 (x^{2} - 10 x + 25) + 2$

Apply the distributive property.

$0 = - 2 x^{2} - 2 (- 10 x) - 2 \cdot 25 + 2$

Simplify.

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Multiply $- 10$ by $- 2$ .

$0 = - 2 x^{2} + 20 x - 2 \cdot 25 + 2$

Multiply $- 2$ by $25$ .

$0 = - 2 x^{2} + 20 x - 50 + 2$

Add $- 50$ and $2$ .

$0 = - 2 x^{2} + 20 x - 48$

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

$x = 4, 6$

x-intercept(s) in point form.

x-intercept(s): $(4, 0), (6, 0)$

Find the y-intercepts.

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

$y = - 2 {((0) - 5)}^{2} + 2$

Solve the equation.

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Remove parentheses.

$y = - 2 {((0) - 5)}^{2} + 2$

Simplify $- 2 {((0) - 5)}^{2} + 2$ .

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Simplify each term.

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Subtract $5$ from $0$ .

$y = - 2 {(- 5)}^{2} + 2$

Raise $- 5$ to the power of $2$ .

$y = - 2 \cdot 25 + 2$

Multiply $- 2$ by $25$ .

$y = - 50 + 2$

Add $- 50$ and $2$ .

$y = - 48$

y-intercept(s) in point form.

y-intercept(s): $(0, - 48)$

List the intersections.

x-intercept(s): $(4, 0), (6, 0)$

y-intercept(s): $(0, - 48)$

Find the X and Y Intercepts -2(x-5)^2+2

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