Question

Write an equation for a parabola with x-intercepts (-4,0) and (2,0) which passes through the point (1,-10).

Answer 1

Explanation:

As the parabola has the given x-intercepts we can write it as

y = a(x - 2)(x + 4) where a is a constant.

Now, it also passes through (1, -10) so we substitute these values:

-10 = a(1 - 2)(1 + 4)

-10 = -5a

a = 2.

So the equation is:

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

y = 2x^2 + 4x -16