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Chapter 1: Q. 116 (page 17)

Make up an equation satisfied by the ordered pairs 2,0,4,0,0,1Compare your equation with a friend鈥檚 equation. Comment on any similarities.

Short Answer

Expert verified

The equation so formed isy=18x2-34x+1

Step by step solution

01

Step 1. Given Information

Given ordered pairs are 2,0,4,0and0,1.

In this exercise, lets determine the function that passes through the given points. As can be seen, the three points are not collinear because two of the points lie on the x-axis while the other one lies in the first quadrant.

02

Step 2. Forming possible equation

Lets assume that the function is parabola.y=ax2+bx+c.

Now, write three satisfied equation by using given coordinate at 2,0and 4,0respectively

i0=a22+2b+c=0鈬�4a+2b+c=0ii0=a42+4b+c=0鈬�16a+4b+c=0

iii1=a02+0b+c=0鈬�c=-1

03

Step 3. Form linear equation by putting c=1

4a+2b=-116a+4b=-1

04

Step 4. Finding the values of a and b

4a+2b=-1----i16a+4b=-1----ii

Solving these two equations by elimination method, we get

a=18,b=-34

05

Step 5. Put the values of a,b,c in the parabola 

y=ax2+bx+cy=18x2-34x+1

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