Find the x and y Intercepts -3x^2-15x+74

$- 3 x^{2} - 15 x + 74$

Step 1

Write $- 3 x^{2} - 15 x + 74$ as an equation.

$y = - 3 x^{2} - 15 x + 74$

Step 2

Find the x-intercepts.

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

$0 = - 3 x^{2} - 15 x + 74$

Solve the equation.

Rewrite the equation as $- 3 x^{2} - 15 x + 74 = 0$ .

$- 3 x^{2} - 15 x + 74 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = - 3$ , $b = - 15$ , and $c = 74$ into the quadratic formula and solve for $x$ .

$\frac{15 \pm \sqrt{{(- 15)}^{2} - 4 \cdot (- 3 \cdot 74)}}{2 \cdot - 3}$

Simplify.

Simplify the numerator.

Raise $- 15$ to the power of $2$ .

$x = \frac{15 \pm \sqrt{225 - 4 \cdot - 3 \cdot 74}}{2 \cdot - 3}$

Multiply $- 4 \cdot - 3 \cdot 74$ .

Multiply $- 4$ by $- 3$ .

$x = \frac{15 \pm \sqrt{225 + 12 \cdot 74}}{2 \cdot - 3}$

Multiply $12$ by $74$ .

$x = \frac{15 \pm \sqrt{225 + 888}}{2 \cdot - 3}$

Add $225$ and $888$ .

$x = \frac{15 \pm \sqrt{1113}}{2 \cdot - 3}$

Multiply $2$ by $- 3$ .

$x = \frac{15 \pm \sqrt{1113}}{- 6}$

Move the negative in front of the fraction.

$x = - \frac{15 \pm \sqrt{1113}}{6}$

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

Simplify the numerator.

Raise $- 15$ to the power of $2$ .

$x = \frac{15 \pm \sqrt{225 - 4 \cdot - 3 \cdot 74}}{2 \cdot - 3}$

Multiply $- 4 \cdot - 3 \cdot 74$ .

Multiply $- 4$ by $- 3$ .

$x = \frac{15 \pm \sqrt{225 + 12 \cdot 74}}{2 \cdot - 3}$

Multiply $12$ by $74$ .

$x = \frac{15 \pm \sqrt{225 + 888}}{2 \cdot - 3}$

Add $225$ and $888$ .

$x = \frac{15 \pm \sqrt{1113}}{2 \cdot - 3}$

Multiply $2$ by $- 3$ .

$x = \frac{15 \pm \sqrt{1113}}{- 6}$

Move the negative in front of the fraction.

$x = - \frac{15 \pm \sqrt{1113}}{6}$

Change the $\pm$ to $+$ .

$x = - \frac{15 + \sqrt{1113}}{6}$

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

Simplify the numerator.

Raise $- 15$ to the power of $2$ .

$x = \frac{15 \pm \sqrt{225 - 4 \cdot - 3 \cdot 74}}{2 \cdot - 3}$

Multiply $- 4 \cdot - 3 \cdot 74$ .

Multiply $- 4$ by $- 3$ .

$x = \frac{15 \pm \sqrt{225 + 12 \cdot 74}}{2 \cdot - 3}$

Multiply $12$ by $74$ .

$x = \frac{15 \pm \sqrt{225 + 888}}{2 \cdot - 3}$

Add $225$ and $888$ .

$x = \frac{15 \pm \sqrt{1113}}{2 \cdot - 3}$

Multiply $2$ by $- 3$ .

$x = \frac{15 \pm \sqrt{1113}}{- 6}$

Move the negative in front of the fraction.

$x = - \frac{15 \pm \sqrt{1113}}{6}$

Change the $\pm$ to $-$ .

$x = - \frac{15 - \sqrt{1113}}{6}$

The final answer is the combination of both solutions.

$x = - \frac{15 + \sqrt{1113}}{6}, - \frac{15 - \sqrt{1113}}{6}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{15 + \sqrt{1113}}{6}, 0), (- \frac{15 - \sqrt{1113}}{6}, 0)$

Step 3

Find the y-intercepts.

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

$y = - 3 {(0)}^{2} - 15 \cdot 0 + 74$

Solve the equation.

Remove parentheses.

$y = - 3 \cdot 0^{2} - 15 \cdot 0 + 74$

Remove parentheses.

$y = - 3 {(0)}^{2} - 15 \cdot 0 + 74$

Simplify $- 3 {(0)}^{2} - 15 \cdot 0 + 74$ .

Simplify each term.

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

$y = - 3 \cdot 0 - 15 \cdot 0 + 74$

Multiply $- 3$ by $0$ .

$y = 0 - 15 \cdot 0 + 74$

Multiply $- 15$ by $0$ .

$y = 0 + 0 + 74$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 74$

Add $0$ and $74$ .

$y = 74$

y-intercept(s) in point form.

y-intercept(s): $(0, 74)$

Step 4

List the intersections.

x-intercept(s): $(- \frac{15 + \sqrt{1113}}{6}, 0), (- \frac{15 - \sqrt{1113}}{6}, 0)$

y-intercept(s): $(0, 74)$

Step 5

Find the x and y Intercepts -3x^2-15x+74

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