Question

On a coordinate plane, a parabola with a dashed boundary line opens down. It goes through (-8, 0), has a vertex at (-6, 2), and goes through (-4, 0). Which inequality in standard form represents the shaded region?

Answer 1

The inequality representing the shaded region of the parabola is y < (1/16)(x + 6)^2 + 2.

Step-by-step explanation:

To represent the shaded region of the parabola on the coordinate plane, we need to find the equation of the parabola. Since the parabola opens down and has a vertex at (-6, 2), the equation can be written as y = a(x + 6)^2 + 2. To find the value of a, we can use the fact that the parabola passes through the points (-8, 0) and (-4, 0).

Plugging in the coordinates (-8, 0) and (-4, 0) into the equation, we get 0 = a(-8 + 6)^2 + 2 and 0 = a(-4 + 6)^2 + 2. Simplifying these equations gives us -32a + 2 = 0 and -8a + 2 = 0. Solving for a, we find a = 1/16.

Therefore, the equation of the parabola is y = (1/16)(x + 6)^2 + 2. To represent the shaded region below the parabola, we need to write the inequality in standard form. The shaded region satisfies y < (1/16)(x + 6)^2 + 2. So the inequality representing the shaded region is y < (1/16)(x + 6)^2 + 2.