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Chapter 10: Q. 307 (page 1238)

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

y=x2-4x+10

Short Answer

Expert verified

There is no x- intercept and y- intercept is the point(0,10).

Step by step solution

01

Given information

The given expression is:y=x2-4x+10

02

Determine the x- intercept.

For xintercept, set y=0 and solve forx.

0=x2-4x+10x2-4x+10=0

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

b2-4ac=(-4)2-(-4)(1)(20)=16-40=-26

Because the value of discriminant is negative, so the equation has no real solution.

There is nox- intercept.

03

Determine the y- intercept.

Substitute x=0and evaluate y(0).

y=(0)2-4(0)+10=0-0+10=10

y- intercept is the point(0,10)

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