Find the x and y Intercepts y=-2x^2+11x+8

$y = - 2 x^{2} + 11 x + 8$

Step 1

Find the x-intercepts.

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

$0 = - 2 x^{2} + 11 x + 8$

Solve the equation.

Rewrite the equation as $- 2 x^{2} + 11 x + 8 = 0$ .

$- 2 x^{2} + 11 x + 8 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = - 2$ , $b = 11$ , and $c = 8$ into the quadratic formula and solve for $x$ .

$\frac{- 11 \pm \sqrt{11^{2} - 4 \cdot (- 2 \cdot 8)}}{2 \cdot - 2}$

Simplify.

Simplify the numerator.

Raise $11$ to the power of $2$ .

$x = \frac{- 11 \pm \sqrt{121 - 4 \cdot - 2 \cdot 8}}{2 \cdot - 2}$

Multiply $- 4 \cdot - 2 \cdot 8$ .

Multiply $- 4$ by $- 2$ .

$x = \frac{- 11 \pm \sqrt{121 + 8 \cdot 8}}{2 \cdot - 2}$

Multiply $8$ by $8$ .

$x = \frac{- 11 \pm \sqrt{121 + 64}}{2 \cdot - 2}$

Add $121$ and $64$ .

$x = \frac{- 11 \pm \sqrt{185}}{2 \cdot - 2}$

Multiply $2$ by $- 2$ .

$x = \frac{- 11 \pm \sqrt{185}}{- 4}$

Simplify $\frac{- 11 \pm \sqrt{185}}{- 4}$ .

$x = \frac{11 \pm \sqrt{185}}{4}$

Simplify the expression to solve for the $+$ portion of the $\pm$ .

Simplify the numerator.

Raise $11$ to the power of $2$ .

$x = \frac{- 11 \pm \sqrt{121 - 4 \cdot - 2 \cdot 8}}{2 \cdot - 2}$

Multiply $- 4 \cdot - 2 \cdot 8$ .

Multiply $- 4$ by $- 2$ .

$x = \frac{- 11 \pm \sqrt{121 + 8 \cdot 8}}{2 \cdot - 2}$

Multiply $8$ by $8$ .

$x = \frac{- 11 \pm \sqrt{121 + 64}}{2 \cdot - 2}$

Add $121$ and $64$ .

$x = \frac{- 11 \pm \sqrt{185}}{2 \cdot - 2}$

Multiply $2$ by $- 2$ .

$x = \frac{- 11 \pm \sqrt{185}}{- 4}$

Simplify $\frac{- 11 \pm \sqrt{185}}{- 4}$ .

$x = \frac{11 \pm \sqrt{185}}{4}$

Change the $\pm$ to $+$ .

$x = \frac{11 + \sqrt{185}}{4}$

Simplify the expression to solve for the $-$ portion of the $\pm$ .

Simplify the numerator.

Raise $11$ to the power of $2$ .

$x = \frac{- 11 \pm \sqrt{121 - 4 \cdot - 2 \cdot 8}}{2 \cdot - 2}$

Multiply $- 4 \cdot - 2 \cdot 8$ .

Multiply $- 4$ by $- 2$ .

$x = \frac{- 11 \pm \sqrt{121 + 8 \cdot 8}}{2 \cdot - 2}$

Multiply $8$ by $8$ .

$x = \frac{- 11 \pm \sqrt{121 + 64}}{2 \cdot - 2}$

Add $121$ and $64$ .

$x = \frac{- 11 \pm \sqrt{185}}{2 \cdot - 2}$

Multiply $2$ by $- 2$ .

$x = \frac{- 11 \pm \sqrt{185}}{- 4}$

Simplify $\frac{- 11 \pm \sqrt{185}}{- 4}$ .

$x = \frac{11 \pm \sqrt{185}}{4}$

Change the $\pm$ to $-$ .

$x = \frac{11 - \sqrt{185}}{4}$

The final answer is the combination of both solutions.

$x = \frac{11 + \sqrt{185}}{4}, \frac{11 - \sqrt{185}}{4}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{11 + \sqrt{185}}{4}, 0), (\frac{11 - \sqrt{185}}{4}, 0)$

Step 2

Find the y-intercepts.

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

$y = - 2 {(0)}^{2} + 11 (0) + 8$

Solve the equation.

Remove parentheses.

$y = - 2 \cdot 0^{2} + 11 (0) + 8$

Remove parentheses.

$y = - 2 {(0)}^{2} + 11 (0) + 8$

Simplify $- 2 {(0)}^{2} + 11 (0) + 8$ .

Simplify each term.

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

$y = - 2 \cdot 0 + 11 (0) + 8$

Multiply $- 2$ by $0$ .

$y = 0 + 11 (0) + 8$

Multiply $11$ by $0$ .

$y = 0 + 0 + 8$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 8$

Add $0$ and $8$ .

$y = 8$

y-intercept(s) in point form.

y-intercept(s): $(0, 8)$

Step 3

List the intersections.

x-intercept(s): $(\frac{11 + \sqrt{185}}{4}, 0), (\frac{11 - \sqrt{185}}{4}, 0)$

y-intercept(s): $(0, 8)$

Step 4

Find the x and y Intercepts y=-2x^2+11x+8

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