Question

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.

x h(x)
-6 15
-5 10
-4 7
-3 6
-2 7
-1 10

What are the vertex and range of h(x)?
Vertex (−4, 7); Range 7 ≤ y ≤ ∞
Vertex (−4, 7); Range ∞ ≤ y ≤ 7
\Vertex (−3, 6); Range 6 ≤ y ≤ ∞
Vertex (−3, 6); Range ∞ ≤ y ≤ 6

Answer 1

(c) Vertex (−3, 6); Range 6 ≤ y ≤ ∞

Explanation:

You want the vertex and range of the quadratic function corresponding to the given table of values.

Range

An appropriate choice of the range description will tell you the correct answer.

The lowest value in the table is h(x) = 6. All other values of h(x) are greater than this, so the range must be ...

6 ≤ y ≤ ∞ . . . . . . . matches choice C

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Additional comment

The coordinates of the lowest point on the graph are the coordinates of the vertex: (-3, 6). That matches choice C also.

Often, no work is necessary other than checking the answer choices for reasonableness.

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