Question

The image of a parabolic lens is projected onto a graph. The image crosses the x-axis at –2 and 3. The point (–1, 2) is also on the parabola. Which equation can be used to model the image of the lens?

y = (x – 2)(x + 3)
y = (x – 2)(x + 3)
y = (x + 2)(x – 3)
y = (x + 2)(x – 3)

Answer 1

Zeros at x = -2 and x = 3 give y = k(x+2)(x-3). Use (-1,2) to find k:
2 = k(1)(-4) = -4k ⇒ k = -1/2.

So the model is y = -(1/2)(x+2)(x-3) (or y = -1/2 x^2 + 1/2 x + 3).