Chapter 2: Q. 81 (page 114)

complete the square of each quadratic expression. Then graph each function using the technique of shifting.
$f (x) = - 3 x^{2} - 12 x - 17$

Short Answer

Expert verified

The graph of the given equation is

Step by step solution

Step 1. Given information

Given expression:

$f (x) = - 3 x^{2} - 12 x - 17$

Step 2. Write the concept

In order to complete the square, we will add or subtract some numbers in order to simplify it

Step 3. Calculation

Let's add and subtract $2^{2}$ on right side therefore,

$f (x) = - 3 x^{2} - 12 x - 17 r e w r i t e t h e e x p r e s s i o n a s = - 3 (x^{2} + 4 x) - 17 A d d i n g & S u b t r a c t i n g 2^{2} i n s i d e p a r e n t h e s i s w e g e t, = - 3 (x^{2} + 4 x + 2^{2} - 2^{2}) - 17 = - 3 {(x + 2)}^{2} + 12 - 17 = - 3 {(x + 2)}^{2} - 5$

Step 4. Graphing using shifting technique

In order to graph the given expression, we need to draw the graph of $f (x) = x^{2}$ i.e.

Step 5. Graphing the actual expression

Replace $x$ by $x + 2$ in the expression $f (x) = x^{2} = {(x + 2)}^{2}$

Now multiply $- 3$ which results in the inverted graph i.e,

Now subtracting $- 5$ from the given expression gives us the result,

$f (x) = - 3 {(x + 2)}^{2} - 5$

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complete the square of each quadratic expression. Then graph each function using the technique of shifting.
$f (x) = - 3 x^{2} - 12 x - 17$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the concept

Step 3. Calculation

Step 4. Graphing using shifting technique

Step 5. Graphing the actual expression

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complete the square of each quadratic expression. Then graph each function using the technique of shifting.f(x)=-3x2-12x-17

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the concept

Step 3. Calculation

Step 4. Graphing using shifting technique

Step 5. Graphing the actual expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Decision Maths

Discrete Mathematics

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

complete the square of each quadratic expression. Then graph each function using the technique of shifting.
$f (x) = - 3 x^{2} - 12 x - 17$