For \(q(x)=-2(x-5)^{2}+7\), identify the vertex-form parameters. Give the vertex and symmetry axis, explain both effects of \(a=-2\) on the graph, and check the vertex by evaluation.

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The vertex is (−5, 7) and the axis is x = −5. In (x − h)², h = 5.

The vertex is (5, 7) and the parabola opens up with the parent-function width. The negative factor reflects it down and 2 makes it narrower.

a = −2, h = 5, and k = 7, so the vertex is (5, 7), the axis is x = 5, and the parabola opens down with a vertical stretch by 2. Also q(5) = 7.

The vertex is (7, 5) and the axis is x = 7. The values h and k have been swapped.

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Curriculum context

Course: Math II
Standard: A-SSE.3.b
Category: Algebra
Domain: Seeing Structure in Expressions
Objective: Complete the square to reveal maximum or minimum values of quadratic functions.
Problem type: Identify a vertex from completed-square form