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Chapter 3: Q. 48 (page 156)

Determine the quadratic function whose graph is given.

Short Answer

Expert verified

The quadratic function whose graph is given is $f (x) = (x - 2)^{2} + 1$ or $f (x) = x^{2} - 4 x + 5$ .

Step by step solution

01

Step 1. Given information.

The given graph is:

02

Step 2. Determine the equation.

The vertex is $(2, 1)$ , so $h = 2$ and $k = 1$ . Substitute these values into equation $f (x) = a (x - h)^{2} + k$ .

$f (x) = a (x - 2)^{2} + 1$

To determine the value of $a$ , we use the fact that $f (0) = 5$ (the y-intercept).

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

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

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

03

Step 3. Conclusion.

The quadratic function whose graph is given is $f (x) = (x - 2)^{2} + 1$ or $f (x) = x^{2} - 4 x + 5$ .

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Most popular questions from this chapter

Graph the function $f$ by starting with the graph of $y = x^{2}$ and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

$f (x) = \frac{1}{4} x^{2}$

In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line .

x	$y = f (x)$
-2	4
-1	1
0	-2
1	-5
2	-8

Graph $y = 2 x - 3 .$

Match each graph to one the following functions.

$f (x) = x^{2} - 1$

Match each graph to one the following functions.

$f (x) = - x^{2} - 1$

See all solutions

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