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Chapter 9: Q71. (page 534)

REASONING The graph of a quadratic function has a vertex at 2,0. One point on the graph is 5,9. Find another point on the graph. Explain how you find it.

Short Answer

Expert verified

Another point on the graph is 鈭�1,9.

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. Graph.

The vertex of the graph of the quadratic function is at2,0 and one point on the graph is 5,9. Graph these two points.

03

Step 3. Explanation.

From the graph, it can be observed that the axis of symmetry cuts the parabola into two equal halves.

First count the spaces over and up from the vertex to the point5,9 and do the same on the opposite side. By doing this we get another point on the graph, that is, point 鈭�1,9.

Therefore, another point on the graph is 鈭�1,9.

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Most popular questions from this chapter

Use a table of values to graph the given equation. State the domain and range.

y=鈭�3x2鈭�x+1

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

Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it.

a2鈭�22a+121

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.

An exponential growth equation isy=C1鈭�rt

MULTIPLE REPRESENTATIONS in this problem, you will investigate solving quadratic equations using tables.

a. ALGEBRAIC Determine the related function for each equation. Copy and complete the table below.

b. GRAPHICAL Graph each related function with a graphing calculator.

c. ANALYTICAL use the table feature on your calculator to determine the zeros of each related function. Record the zeros in the table above. Also, record the values of the function one unit less than and one unit more than each zero.

d. VERBAL Compare the signs of the function values for x values just before and just after a zero. What happens to the sign of the function value before and after a zero?
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