Find the x and y Intercepts -2x^2+12x-10

$- 2 x^{2} + 12 x - 10$

Step 1

Write $- 2 x^{2} + 12 x - 10$ as an equation.

$y = - 2 x^{2} + 12 x - 10$

Step 2

Find the x-intercepts.

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

$0 = - 2 x^{2} + 12 x - 10$

Solve the equation.

Rewrite the equation as $- 2 x^{2} + 12 x - 10 = 0$ .

$- 2 x^{2} + 12 x - 10 = 0$

Factor the left side of the equation.

Factor $- 2$ out of $- 2 x^{2} + 12 x - 10$ .

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

$- 2 x^{2} + 12 x - 10 = 0$

Factor $- 2$ out of $12 x$ .

$- 2 x^{2} - 2 (- 6 x) - 10 = 0$

Factor $- 2$ out of $- 10$ .

$- 2 x^{2} - 2 (- 6 x) - 2 \cdot 5 = 0$

Factor $- 2$ out of $- 2 (x^{2}) - 2 (- 6 x)$ .

$- 2 (x^{2} - 6 x) - 2 \cdot 5 = 0$

Factor $- 2$ out of $- 2 (x^{2} - 6 x) - 2 (5)$ .

$- 2 (x^{2} - 6 x + 5) = 0$

Factor.

Factor $x^{2} - 6 x + 5$ 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 $5$ and whose sum is $- 6$ .

$- 5, - 1$

Write the factored form using these integers.

$- 2 ((x - 5) (x - 1)) = 0$

Remove unnecessary parentheses.

$- 2 (x - 5) (x - 1) = 0$

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

$x - 5 = 0$

$x - 1 = 0$

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

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

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

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

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

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The final solution is all the values that make $- 2 (x - 5) (x - 1) = 0$ true.

$x = 5, 1$

x-intercept(s) in point form.

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

Step 3

Find the y-intercepts.

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

$y = - 2 {(0)}^{2} + 12 (0) - 10$

Solve the equation.

Remove parentheses.

$y = - 2 \cdot 0^{2} + 12 (0) - 10$

Remove parentheses.

$y = - 2 {(0)}^{2} + 12 (0) - 10$

Simplify $- 2 {(0)}^{2} + 12 (0) - 10$ .

Simplify each term.

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

$y = - 2 \cdot 0 + 12 (0) - 10$

Multiply $- 2$ by $0$ .

$y = 0 + 12 (0) - 10$

Multiply $12$ by $0$ .

$y = 0 + 0 - 10$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 10$

Subtract $10$ from $0$ .

$y = - 10$

y-intercept(s) in point form.

y-intercept(s): $(0, - 10)$

Step 4

List the intersections.

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

y-intercept(s): $(0, - 10)$

Step 5

Find the x and y Intercepts -2x^2+12x-10

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