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? y > 2x2 + 6x – 36 y > 2x2 – 6x – 36

Answer 1

The inequality in standard form 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:

To represent the region greater than the quadratic function with zeros –3 and 6 and includes the point (–2, –16) on the boundary line, we use the inequality y > 2x^2 + 6x – 36.

To determine if the point (–2, –16) is on the boundary line, we substitute the x and y values into the quadratic function: -16 > 2(-2)^2 + 6(-2) - 36.

Simplifying this equation, we get -16 > 8 - 12 - 36, which becomes -16 > -40. Since this is true, the point (–2, –16) is on the boundary line.