Question

Write the formula for the parabola that has x- intercepts (3,0) and (8,0), and y- intercept (0,−2)

Answer 1

(-1/12)(x-3)(x-8)

or

`-(x^2-11x+24)/(12)`

Explanation:

If something has x intercepts of (3,0) and (8,0) we can write the following

y=(x-3)(x-8)

To make the y intercept (0,-2) we will mulitply this by some constant, a

y=a(x-3)(x-8)

to solve for a set y= -2 and x=0

a(0-3)(0-8)= -2

a(-3)(-8)= -2

24a= -2

a= -1/12

Which means our final equation is

(-1/12)(x-3)(x-8)

which in standard form is equal to

`-(x^2-11x+24)/(12)`