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Chapter 3: Q. 49 (page 156)

Determine the quadratic function whose graph is given.

Short Answer

Expert verified

The quadratic function whose graph is given is f(x)=-(x+3)2+5or f(x)=-x2-6x-4.

Step by step solution

01

Step 1. Given information.

The given graph is:

02

Step 2. Determine the equation.

The vertex is (-3,5), so h=-3and k=5. Substitute these values into equation f(x)=a(x-h)2+k.

f(x)=a(x+3)2+5

To determine the value of a, we use the fact that f(0)=-4(the y-intercept).

-4=a(0+3)2+5-4-5=9a-9=9a-1=a

Substitute a=-1in f(x)=a(x+3)2+5.

f(x)=-1(x+3)2+5f(x)=-(x+3)2+5f(x)=-x2-6x-9+5f(x)=-x2-6x-4

03

Step 3. Conclusion.

The quadratic function whose graph is given isf(x)=-(x+3)2+5 or f(x)=-x2-6x-4.

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Most popular questions from this chapter

To complete the square of x2-5x, you add the number _______.

The daily revenue R achieved by selling x boxes of candy is figured to be R(x)=9.5x-0.04x2The daily cost C of selling x boxes of candy is C(x)=1.25x+250.

(a) How many boxes of candy must the firm sell to maximize revenue? What is the maximum revenue?

(b) Profit is given as P(x) = R(x) - C(x). What is the profit function?

(c) How many boxes of candy must the firm sell to maximize profit? What is the maximum profit?

(d) Provide a reasonable explanation as to why the answers found in parts (a) and (c) differ. Explain why a quadratic function is a reasonable model for revenue.

Show that the inequality (x-2)2>0has one real number that is not a solution.

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

Find the slope of the line joining the points(2,5) and(-1,3).
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