Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 9.121 (page 958)

Graph $f (x) = 鈭� 3 x^{2} + 12 x 鈭� 4$ by using transformations.

Short Answer

Expert verified

The graph of the given function is:

Step by step solution

Step 1. Given Information

The given function is $f (x) = - 3 x^{2} + 12 x - 4$

Step 2. Separate the x term from the constant.

First, separate the xterm from the constant and factor, we get:

$f (x) = - 3 x^{2} + 12 x - 4 f (x) = - 3 (x^{2} - 4 x) - 4$

Step 3. Complete the square

Now, Take half of $4$ and then square it, we get:

localid="1645293331707" ${(\frac{1}{2} 路 - 4)}^{2} = 4$

So, $4$ will complete the square.

Step 4. Write in the required form

The constant $4$ completes the square and then we have to subtract $- 3 脳 4 = - 12$ from the constant.

$f (x) = - 3 (x^{2} - 4 x + 4) - 4 - (- 12) f (x) = - 3 {(x - 2)}^{2} + 8$

Step 5. Graph the function

Looking at the h, k values, we see the graph will take the graph of $y = x^{2}$ and shift it to the right $2$ units and up $8$ units and also multiply y-values in the parabola by $- 3$ . The parabola will be downwards because the leading coefficient is negative.

The graph of the function is given as:

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91影视

Graph $f (x) = 鈭� 3 x^{2} + 12 x 鈭� 4$ by using transformations.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Separate the x term from the constant.

Step 3. Complete the square

Step 4. Write in the required form

Step 5. Graph the function

One App. One Place for Learning.

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91影视

Graph f(x)=鈭�3x2+12x鈭�4by using transformations.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Separate the x term from the constant.

Step 3. Complete the square

Step 4. Write in the required form

Step 5. Graph the function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Calculus

Pure Maths

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Graph $f (x) = 鈭� 3 x^{2} + 12 x 鈭� 4$ by using transformations.