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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 $f (x) = - (x + 3)^{2} + 5$ or $f (x) = - x^{2} - 6 x - 4$ .

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 $h = - 3$ and $k = 5$ . 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).

$\begin{array}{rcl} - 4 & = & a (0 + 3)^{2} + 5 \\ - 4 - 5 & = & 9 a \\ - 9 & = & 9 a \\ - 1 & = & a \end{array}$

Substitute $a = - 1$ in $f (x) = a (x + 3)^{2} + 5$ .

$f (x) = - 1 (x + 3)^{2} + 5 f (x) = - (x + 3)^{2} + 5 f (x) = - x^{2} - 6 x - 9 + 5 f (x) = - x^{2} - 6 x - 4$

03

Step 3. Conclusion.

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

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Most popular questions from this chapter

Find the average rate of change of $f (x) = 3 x^{2} - 2$ from 2 to 4.

In Problems 25–32, use the given functions f and g.

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