Question

A student draws two parabolas both parabolas cross the x axis at (-4,0) and (6,0) the y intercept of the first parabolas is (0,-12). The y intercept of the second parabola is (0,-24) what is the positive difference between the a values for the two functions that describe the parabolas

Answer 1

0.5

Explanation:

Answer 2

The positive difference between the a values is 0.5

Explanation:

we know that

Both parabolas cross the x axis at (-4,0) and (6,0)

so

The general equation is

`y=a(x+4)(x-6)`

Find the value of a in the first parabola

The y-intercept is (0,-12)

so

For
`x=0, y=-12`

substitute

`y=a(x+4)(x-6)`

`-12=a(0+4)(0-6)`

`-12=a(-24)`

`a=0.5`

Find the value of a in the second parabola

The y-intercept is (0,-24)

so

For
`x=0, y=-24`

substitute

`y=a(x+4)(x-6)`

`-24=a(0+4)(0-6)`

`-24=a(-24)`

`a=1`

Find the positive difference between the a values for the two functions

so

`1-0.5=0.5`