Question

write a quadratic function that has a graph that contains the following points, (-2, 0), (4, -12), (5,0).

Answer 1

f(x) = 2x^2 - 6x - 20.

Explanation:

(-2, 0) and (5, 0) are 2 zeroes of the function so we can write the function as

f(x) = a(x + 2)(x - 5) where a is a constant.

Now as (4, -12) is a point on the graph:

-12 = a(4 + 2)(4 - 5)

-12 = a * 6 * -1

-6a = -12

a = 2.

So f(x) = 2(x + 2)(x - 5)

f(x) = 2x^2 - 6x - 20.