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Chapter 10: Q. 308 (page 1238)

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

y=-5x2-30x-46

Short Answer

Expert verified

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

Step by step solution

01

Given information

The given expression is:y=-5x2-30x-46

02

Determine the x- intercept.

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

0=-5x2-30x-46-5x2-30x-46=0

03

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

b2-4ac=(-30)2-(-4)(-5)(-46)=900-920=-20

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

There is nox- intercept.

04

Determine the y- intercept.

Substitute x=0and evaluate y(0).

y=-5(0)2-30(0)-46=-0-0-46=-46

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

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