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Chapter 6: Q2. (page 290)

Identify the vertex and the equation of the axis of symmetry for each function graphed below.

Short Answer

Expert verified

a. The equation of axis of symmetry is x=2 and the vertex is 2,1.

b. The equation of axis of symmetry is x=-3 and the vertex is -3,-2.

Step by step solution

01

aStep 1. Use the concept.

All parabolas have an axis of symmetry. If you were to fold a parabola along its axis of symmetry, the portions of the parabola on either side of this line would match.

The point at which the axis of symmetry intersects a parabola is called the vertex.

02

Step 2. Given Information.

03

Step 3. Solution.

Clearly, the graph is symmetric around x=2 and the graph of parabola intersects the axis of symmetry at 2,1.

So, the equation of axis of symmetry is x=2 and the vertex is 2,1.

04

bStep 1. Use the concept.

All parabolas have an axis of symmetry. If you were to fold a parabola along its axis of symmetry, the portions of the parabola on either side of this line would match.

The point at which the axis of symmetry intersects a parabola is called the vertex.

05

Step 2. Given Information.

The graph is:

06

Step 3. Solution.

Clearly, the graph is symmetric around x=-3 and the graph of parabola intersects the axis of symmetry at -3,-2.

So, the equation of axis of symmetry is x=-3 and the vertex is -3,-2.

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Most popular questions from this chapter

Complete parts a-c for each quadratic function.

  1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
  2. Make a table of values that includes the vertex.
  3. Use this information to graph the function.

f(x)=x2-4x+4

Simplify

i14

Explain how you can estimate the solutions of a quadratic equation by examining the graph of its related function.

An object is fired straight up from the top of a 200-foot tower at a velocity of 80 feet per second. The height h(t) of the object t seconds after firing is given by h(t)=-16t2+80t+200. Find the maximum height reached by the object and the time that the height is reached.

Complete parts a-c for each quadratic function.

a. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.

b. Make a table of values that includes the vertex.

c. Use this information to graph the function.

f(x)=-0.25x2-3x
See all solutions

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