(Please Help) The vertex of a parabola is (−2,8) and its y-intercept is (0,4). The parabola is the boundary of a quadratic inequality. The boundary is drawn with a solid line, and the exterior of the parabola is shaded.

What is the inequality represented?

(i got it graphed like what i have already but I don't know if its right even thought i gotten it)

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joaobezerra joaobezerra · Answer 1 · 2022-09-09T20:23:37+02:00

Using the equation of the parabola, the inequality represented is:

y ≥ -(x + 2)² + 8.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

For this problem, the vertex is at (-2,8), hence:

h = -2, k = 8.

y = a(x + 2)² + 8.

The y-intercept is of (0,4), when when x = 0, y = 4, which we use to find a as follows:

4 = 4a + 8

4a = -4

a = -1.

Hence the parabola is:

y = -(x + 2)² + 8.

The exterior of the parabola is shaded, that is, the part that is above the concave down parabola, hence the inequality is:

y ≥ -(x + 2)² + 8.

More can be learned about the equation of a parabola at https://brainly.com/question/24737967

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