Question

In the following exercises, find the x- andy-intercepts.

$y=-5x^2-30x-46$

Short answer

There is no x- intercept and y- intercept is the point$(0,-46)$.

Step-by-step solution

Given information

The given expression is:$y=-5x^2-30x-46$

Determine the x- intercept.

For x- intercept, set $y=0$and solve for x.

$$\begin{gathered} 0=-5x^2-30x-46 \\ -5x^2-30x-46=0 \end{gathered}$$

Find the value of the discriminant to predict the number of solution.

$$\begin{gathered} b^2-4ac={(-30)}^2-(-4)(-5)(-46) \\ =900-920 \\ =-20 \end{gathered}$$

Because the value of discriminant is negative, so the solution is not real.

There is nox- intercept.

Determine the y- intercept.

Substitute $x=0$and evaluate $y\left(0\right)$.

$$\begin{gathered} y=-5{\left(0\right)}^2-30\left(0\right)-46 \\ =-0-0-46 \\ =-46 \end{gathered}$$

y- intercept is the point$(0,-46)$.