Question

Which inequality in vertex form represents the region less than the quadratic function with vertex (-2, 2) and

includes the point (-4, 14) on the boundary?

Answer 1

(a) y < 3(x +2)² +2

Explanation:

You want to know the inequality representing the region less than the quadratic with vertex (-2, 2) and containing the point (-4, 14).

Vertex form

The vertex form equation for a quadratic with vertex (h, k) and some scale factor 'a' is ...

y = a(x -h)² +k

For the given vertex (-2, 2), the boundary line equation is ...

y = a(x -(-2))² +2 = a(x +2)² +2

Scale factor

The value of 'a' is positive when the curve opens upward.

Here, the point (-4, 14) has a y-value greater than that of the vertex, so we know the curve opens upward (a > 0).

The only reasonable answer choice is ...

y < 3(x +2)² +2