Q. 50 Determine the quadratic function... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 3: Q. 50 (page 156)

Determine the quadratic function whose graph is given.

Short Answer

Expert verified

The quadratic function whose graph is given is $f (x) = - (x - 2)^{2} + 3$ or $f (x) = - x^{2} + 4 x - 1$ .

Step by step solution

Step 1. Given information.

The given graph is:

Step 2. Determine the equation.

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

$f (x) = a (x - 2)^{2} + 3$

To determine the value of $a$ , we use the fact that $f (0) = - 1$ (the y-intercept).

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

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

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

Step 3. Conclusion.

The quadratic function whose graph is given is $f (x) = - (x - 2)^{2} + 3$ or $f (x) = - x^{2} + 4 x - 1$ .

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x	$y = f (x)$
-2	-26
-1	-4
0	2
1	-2
2	-10

91影视

Determine the quadratic function whose graph is given.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the equation.

Step 3. Conclusion.

One App. One Place for Learning.

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