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Chapter 9: Q. 246 (page 944)

In the following exercises, find the intercepts of the parabola whose function is given.

f(x)=鈭�3x2+x鈭�1

Short Answer

Expert verified

The y-intercept is (0,-1)and there are no x-intercept.

Step by step solution

01

Step 1. Given and explanation 

We are given a function f(x)=鈭�3x2+x鈭�1.

The y intercept is given by putting x=0 and the x intercept is given by putting the function equals to zero.

02

Step 2. Finding y- intercept

Putting x=0in the given function, we get

role="math" f(0)=-3(0)2+(0)-1f(0)=0+0-1f(0)=-1

Hence they-intercept is -1.

03

Step 3. Finding x- intercept

Putting f(x)=0, we get

role="math" localid="1645182770704" f(x)=0-3x2+x-1=03x2-x+1=0

Finding the value of discriminant,

b2-4ac=(-1)2-4(3)(1)=1-12=-11<0

Hence the given function has no x-intercept.

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