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Chapter 9: Q73. (page 534)

REASONING Provide a counterexample to the following statement. The vertex of a parabola is always the minimum of the graph.

Short Answer

Expert verified

Counterexample isy=−x2+2 with vertex is maximum of the graph.

Step by step solution

01

Step 1. Define Vertex.

The axis of symmetry intersects a parabola at only one point is called vertex.

02

Step 2. Counterexample.

Consider the quadratic equation, y=−x2+2. It has a vertex at 0,2. Comparing it with the standard form of quadratic equation, a=−1<0. Therefore, the parabola opens downward and the vertex is the maximum of the graph.

03

Step 3. Graph.

Make a graph representing the above-mentioned equation.

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CHALLENGE Using the axis of symmetry and one x-intercept, write an equation for the graph shown.
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