Find the x and y Intercepts y=4x^2-5x-4

$y = 4 x^{2} - 5 x - 4$

Find the x-intercepts.

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

$0 = 4 x^{2} - 5 x - 4$

Solve the equation.

Rewrite the equation as $4 x^{2} - 5 x - 4 = 0$ .

$4 x^{2} - 5 x - 4 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 4$ , $b = - 5$ , and $c = - 4$ into the quadratic formula and solve for $x$ .

$\frac{5 \pm \sqrt{{(- 5)}^{2} - 4 \cdot (4 \cdot - 4)}}{2 \cdot 4}$

Simplify.

Simplify the numerator.

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

$x = \frac{5 \pm \sqrt{25 - 4 \cdot 4 \cdot - 4}}{2 \cdot 4}$

Multiply $- 4$ by $4$ .

$x = \frac{5 \pm \sqrt{25 - 16 \cdot - 4}}{2 \cdot 4}$

Multiply $- 16$ by $- 4$ .

$x = \frac{5 \pm \sqrt{25 + 64}}{2 \cdot 4}$

Add $25$ and $64$ .

$x = \frac{5 \pm \sqrt{89}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{5 \pm \sqrt{89}}{8}$

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

Simplify the numerator.

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

$x = \frac{5 \pm \sqrt{25 - 4 \cdot 4 \cdot - 4}}{2 \cdot 4}$

Multiply $- 4$ by $4$ .

$x = \frac{5 \pm \sqrt{25 - 16 \cdot - 4}}{2 \cdot 4}$

Multiply $- 16$ by $- 4$ .

$x = \frac{5 \pm \sqrt{25 + 64}}{2 \cdot 4}$

Add $25$ and $64$ .

$x = \frac{5 \pm \sqrt{89}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{5 \pm \sqrt{89}}{8}$

Change the $\pm$ to $+$ .

$x = \frac{5 + \sqrt{89}}{8}$

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

Simplify the numerator.

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

$x = \frac{5 \pm \sqrt{25 - 4 \cdot 4 \cdot - 4}}{2 \cdot 4}$

Multiply $- 4$ by $4$ .

$x = \frac{5 \pm \sqrt{25 - 16 \cdot - 4}}{2 \cdot 4}$

Multiply $- 16$ by $- 4$ .

$x = \frac{5 \pm \sqrt{25 + 64}}{2 \cdot 4}$

Add $25$ and $64$ .

$x = \frac{5 \pm \sqrt{89}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{5 \pm \sqrt{89}}{8}$

Change the $\pm$ to $-$ .

$x = \frac{5 - \sqrt{89}}{8}$

The final answer is the combination of both solutions.

$x = \frac{5 + \sqrt{89}}{8}, \frac{5 - \sqrt{89}}{8}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{5 + \sqrt{89}}{8}, 0), (\frac{5 - \sqrt{89}}{8}, 0)$

Find the y-intercepts.

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

$y = 4 {(0)}^{2} - 5 \cdot 0 - 4$

Solve the equation.

Remove parentheses.

$y = 4 \cdot 0^{2} - 5 \cdot 0 - 4$

Remove parentheses.

$y = 4 {(0)}^{2} - 5 \cdot 0 - 4$

Simplify $4 {(0)}^{2} - 5 \cdot 0 - 4$ .

Simplify each term.

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

$y = 4 \cdot 0 - 5 \cdot 0 - 4$

Multiply $4$ by $0$ .

$y = 0 - 5 \cdot 0 - 4$

Multiply $- 5$ by $0$ .

$y = 0 + 0 - 4$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 4$

Subtract $4$ from $0$ .

$y = - 4$

y-intercept(s) in point form.

y-intercept(s): $(0, - 4)$

List the intersections.

x-intercept(s): $(\frac{5 + \sqrt{89}}{8}, 0), (\frac{5 - \sqrt{89}}{8}, 0)$

y-intercept(s): $(0, - 4)$

Find the x and y Intercepts y=4x^2-5x-4

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