Chapter 3: Q. 83 (page 157)

Suppose that $f (x) = x^{2} + 4 x - 21 .$
(a) What is the vertex of $f$ ?
(b) What are the $x$ -intercepts of the graph of $f$ ?
(c) Solve $f (x) = - 21$ for x. What points are on the graph of $f$ ?
(d) Use the information obtained in parts (a) – (c) to graph $f (x) = x^{2} + 4 x - 21 .$

Short Answer

Expert verified

(a) Vertex is $(- 2, - 25) .$

(b) $x$ - intercept is $x = 3, x = 7 .$

(d) The graph of $f (x)$ is,

Step by step solution

Part (a) Step 1. Given information

It is given that $f (x) = x^{2} + 4 x - 21,$ we need to write the vertex of $f .$

Step 2. Simplify

$f (x) = x^{2} + 4 x - 21 .$

$f (x) = x^{2} + 4 x + 4 - 4 - 21 .$

$= {(x + 2)}^{2} - 25 .$

The vertex is $(- 2, - 25) .$

Part (b) Step 1. Given information

It is given that $f (x) = x^{2} + 4 x - 21,$ we need to write the $x$ - intercept of the graph of $f .$

Step 2. Simplify

Put $f (x) = 0 .$

$x^{2} + 4 x - 21 = 0 .$

$x = \frac{- 4 \pm \sqrt{4^{2} - 4 \cdot 1 (- 21)}}{2 \cdot 1} .$

$= \frac{- 4 \pm \sqrt{16 + 84}}{2} .$

$= \frac{- 4 \pm \sqrt{100}}{2} .$

$= \frac{- 4 \pm 10}{2} .$

$x = \frac{- 4 + 10}{2} = 3, x = \frac{- 4 - 10}{2} = 7 .$

$x$ -intercept is $x = 3, x = 7 .$

Part (c) Step 1. Given information

It is given that $f (x) = x^{2} + 4 x - 21,$ we need to solve $f (x) = - 21$ for $x$ amd also the points are on the graph.

Step 2. Solving

$f (x) = - 21 .$

$x^{2} + 4 x - 21 = - 21 .$

$x^{2} + 4 x = 0 .$

$x (x + 4) = 0 .$

$x 0, x + 4 = 0 .$

$x = - 4 .$

When $x = 0 o r x = - 4$ , the values of the function is $- 21 .$

The points $(0, - 21), (- 4, - 21)$ are on the graph of the function $f .$

Part (d) Step 1. Given information

It is given that $f (x) = x^{2} + 4 x - 21,$ we need to use the information of part a-c to graph the $f (x) .$

Step 2. Graph of fx

The graph of

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Suppose that $f (x) = x^{2} + 4 x - 21 .$
(a) What is the vertex of $f$ ?
(b) What are the $x$ -intercepts of the graph of $f$ ?
(c) Solve $f (x) = - 21$ for x. What points are on the graph of $f$ ?
(d) Use the information obtained in parts (a) – (c) to graph $f (x) = x^{2} + 4 x - 21 .$

Short Answer

Step by step solution

Part (a) Step 1. Given information

Step 2. Simplify

Part (b) Step 1. Given information

Step 2. Simplify

Part (c) Step 1. Given information

Step 2. Solving

Part (d) Step 1. Given information

Step 2. Graph of fx

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Suppose that fx=x2+4x-21.(a) What is the vertex of f?(b) What are the x-intercepts of the graph of f? (c) Solvefx=-21for x. What points are on the graph of f? (d) Use the information obtained in parts (a) – (c) to graphfx=x2+4x-21.

Short Answer

Step by step solution

Part (a) Step 1. Given information

Step 2. Simplify

Part (b) Step 1. Given information

Step 2. Simplify

Part (c) Step 1. Given information

Step 2. Solving

Part (d) Step 1. Given information

Step 2. Graph of fx

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Discrete Mathematics

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Statistics

Study anywhere. Anytime. Across all devices.

Suppose that $f (x) = x^{2} + 4 x - 21 .$
(a) What is the vertex of $f$ ?
(b) What are the $x$ -intercepts of the graph of $f$ ?
(c) Solve $f (x) = - 21$ for x. What points are on the graph of $f$ ?
(d) Use the information obtained in parts (a) – (c) to graph $f (x) = x^{2} + 4 x - 21 .$