Chapter 9: Q54. (page 532)

Graph the function.
$y = - 2 x^{2} - 8 x + 2$

Short Answer

Expert verified

The graph of the function $y = - 2 x^{2} - 8 x + 2$ is

Step by step solution

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, $y = a x^{2} + b x + c$ , where, $a \neq 0$ is called the standard form of the quadratic function.

Step 2. Define the maximum or minimum point of the function y=ax2+bx+c.

The graph of the function $y = a x^{2} + b x + c$

Opens upward and has a minimum value at $x = - \frac{b}{2 a}$ , when $a > 0$ .

Opens downward and has a maximum value at $x = - \frac{b}{2 a}$ , when $a < 0$ .

Step 3. Define y-intercept of the function y=ax2+bx+c.

The $y$ -intercept of the function $y = a x^{2} + b x + c$ is always at $c$ .

Step 4. Plot the graph of the function y=−2x2−8x+2.

Compare the quadratic function $y = - 2 x^{2} - 8 x + 2$ with the standard quadratic function $y = a x^{2} + b x + c$ .

$a = - 2, b = - 8, c = 2$

Substitute $a = - 2$ and $b = - 8$ in $x = - \frac{b}{2 a}$ .

$x = - (\frac{- 8}{2 (- 2)}) x = - (\frac{- 8}{- 4}) x = - (2) x = - 2$

Since, $a < 0$ .

So, the graph opens downward and has a maximum value at $x = - 2$ .

Since, the $y$ -intercept is given by $c$ .

So, the $y$ -intercept is 2.

The graph of the function $y = - 2 x^{2} - 8 x + 2$ is shown below.

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Graph the function.
$y = - 2 x^{2} - 8 x + 2$

Short Answer

Step by step solution

Step 1. Define the standard form of the quadratic function.

Step 2. Define the maximum or minimum point of the function y=ax2+bx+c.

Step 3. Define y-intercept of the function y=ax2+bx+c.

Step 4. Plot the graph of the function y=−2x2−8x+2.

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Graph the function.y=−2x2−8x+2

Short Answer

Step by step solution

Step 1. Define the standard form of the quadratic function.

Step 2. Define the maximum or minimum point of the function y=ax2+bx+c.

Step 3. Define y-intercept of the function y=ax2+bx+c.

Step 4. Plot the graph of the function y=−2x2−8x+2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Calculus

Applied Mathematics

Logic and Functions

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Graph the function.
$y = - 2 x^{2} - 8 x + 2$