Question

Which inequality in standard form represents the region greater than the quadratic function with zeros –3 and 6 and includes the point (–2, –16) on the boundary line?

a) y > 2x^2 + 6x – 36
b) y > 2x^2 – 6x – 36
c) y ≥ 2x^2 + 6x – 36
d) y ≥ 2x^2 – 6x – 36

Answer 1

The inequality that represents the region greater than the quadratic function with zeros -3 and 6 and includes the point (-2, -16) on the boundary line is y > 2x^2 + 6x - 36.

Step-by-step explanation:

The quadratic function with zeros -3 and 6 can be written in factored form as y = a(x + 3)(x - 6), where 'a' represents the leading coefficient. To determine which inequality represents the region greater than the quadratic function and includes the point (-2, -16), we need to find the value of 'a' that satisfies this condition.

Substituting the point (-2, -16) into the equation, we get:

-16 = a(-2 + 3)(-2 - 6)

-16 = a(1)(-8)

-16 = -8a

a = 2

Therefore, the inequality that represents the region greater than the quadratic function is y > 2x^2 + 6x - 36.