Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Determine the quadratic function whose graph is given.

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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

Find Study Materials for

Create Study Materials

Select your language

Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Determine the quadratic function whose graph is given.

Step by Step Solution

Step 1. Given information.

Step 2. Determine the equation.

Step 3. Conclusion.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Determine the quadratic function whose graph is given.

Step by Step Solution

Step 1. Given information.

Step 2. Determine the equation.

Step 3. Conclusion.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths