Create a function whose graph has x intercepts at (-2,0) and (4,0) and a y intercept of (0,-4) leave in expanded form

Answer 1

I thought about this and Michael's answer helped.

given just the two y=0 values of x, we can find quadradic

y=a(x+2)(x-4)

when x = 0

-4=a*(-8)

a=1/2

y=(1/2)*(x+2)(x-4)=x²/2-x-4

Answer 2

If you have x intercepts at (x₁, 0), (x₂, 0), (x₃, 0)... then a possible function with those intercepts is:

y = a(x - x₁)(x - x₂)(x - x₃)...

For example:

Say we have x intercepts at (1, 0), (4, 0), (-2, 0) and y intercept at (0, 3)

A possible function containing those x-intercepts is y = a(x - 1)(x - 4)(x + 2)

To do with the y intercept, we'll plug in the y-intercept and solve for a

(3) = a(0-1)(0-4)(0+2)

3 = a(-1)(-4)(2)

3 = a(8)

a = 3/8 = 0.375

Therefore the function is y = 0.375(x - 1)(x - 4)(x + 2)