Question

PLEASE HELP

The function h(x) is a continuous quadratic function with a domain of all real numbers. The table lists some of the points on the function.

(Graph was Here)

What are the vertex and range of h(x)?

A. Vertex (−4, 4); Range ∞ ≤ y ≤ 4
B. Vertex (−4, 4); Range 4 ≤ y ≤ ∞
C. Vertex (−3, 3); Range 3 ≤ y ≤ ∞
D. Vertex (−3, 3); Range ∞ ≤ y ≤ 3

Answer 1

C. Vertex (−3, 3); Range 3 ≤ y ≤ ∞

Explanation:

The graph of a quadratic function h(x) is symmetric about the axis of symmetry.

The axis of symmetry is a vertical line that divides the parabola into two congruent halves and passes through the vertex.

The axis of symmetry is the x-value of the vertex.

Vertex

From the table of values, we can see that the y-values of function h(x) are symmetric either side of h(x) = 3. Therefore, the axis of symmetry is x = -3 and the vertex is (-3, 3).

Range

The range of a function is the set of all possible output values (y-values).

From the table, we can see that the minimum y-value is y = 3, so the range of the function is therefore 3 ≤ y ≤ ∞.