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Chapter 3: Q. 6 (page 175)

Determine the quadratic function for the given graph.

Short Answer

Expert verified

The quadratic function isf(x)=2(x-1)2-32.

Step by step solution

01

Step 1. Given information.

Determine the quadratic function for the given graph.

02

Step 2. Find the quadratic function.

If the vertex h,kand one point on the graph of a quadratic function are known, then we can write

f(x)=a(x-h)2+k

From the given graph, vertex is 1,-32so,h=1andk=-32

Now substitute these values into the equation

f(x)=a(x-h)2+k

To determine the value of a, use a fact that point5,0 is on the graph.

03

Step 3. substitute the values.

f(5)=a5-12-320=16a-3216a=32a=2

Substitute the value of ainto the function.

f(x)=a(x-h)2+k=2(x-1)2-32

04

Step 4. Conclusion. 

The quadratic function isf(x)=2(x-1)2-32.

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Most popular questions from this chapter

If f(x)=14x-3,then

(a) Determine the slope and y-intercept of each function.

(b) Use the slope and y-intercept to graph the linear function.

(c) Determine the average rate of change of each function.

(d) Determine whether the linear function is increasing, decreasing, or constant

Find a quadratic function whose x-intercepts are -4 and 2 and whose range is[-18,鈭�)

If the independent variable in a line of best fit y=-0.008x+14is credit score, and the dependent variable is the interest rate on a used car loan, then the slope is interpreted as 鈥渋f credit score increases by 1 point, the interest rate will (increase/decrease) by percent, on average.

Graph the function fby starting with the graph of y=x2and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

Hint: If necessary, write fin the form f(x)=a(x-h)2+k.

f(x)=x2+4x+2

If G(x)=-2,then

(a) Determine the slope and y-intercept of each function.

(b) Use the slope and y-intercept to graph the linear function.

(c) Determine the average rate of change of each function.

(d) Determine whether the linear function is increasing, decreasing, or constant.
See all solutions

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