Chapter 9: Q. 9.86 (page 924)

Determine whether the graph of each function is a parabola that opens upward or downward:
ⓐ $f (x) = - 2 x^{2} - 2 x - 3$
ⓑ $f (x) = 5 x^{2} - 2 x - 1$

Short Answer

Expert verified

ⓐ The parabola will open downward for $f (x) = - 2 x^{2} - 2 x - 3$
ⓑ The parabola will open upward for $f (x) = 5 x^{2} - 2 x - 1$

Step by step solution

Step 1. Given Information

We want to determine whether the graph of each function is a parabola that opens upward or downward:

ⓐ $f (x) = - 2 x^{2} - 2 x - 3$

ⓑ $f (x) = 5 x^{2} - 2 x - 1$

We know that Parabola Orientation:

For the graph of the quadratic function $f (x) = a x^{2} + b x + c$ , if

a > 0, the parabola opens upwards.
a < 0, the parabola opens downwards.

Part (a) Step 1. Solve for f (x) = −2x2 − 2x − 3

Find the value of “a”.

$f (x) = a x^{2} + b x + c$

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

$a = - 2 < 0$

Since the “a” is negative, the parabola will open downward.

Part (b) Step 1. Solve for f (x) = 5x2 − 2x − 1

Find the value of “a”.

$f (x) = a x^{2} + b x + c$

role="math" localid="1646322415764" $f (x) = 5 x^{2} - 2 x - 1 a = 5 > 0$

Since the “a” is positive, the parabola will open upward.

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Determine whether the graph of each function is a parabola that opens upward or downward:
ⓐ $f (x) = - 2 x^{2} - 2 x - 3$
ⓑ $f (x) = 5 x^{2} - 2 x - 1$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Solve for f (x) = −2x2 − 2x − 3

Part (b) Step 1. Solve for f (x) = 5x2 − 2x − 1

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Determine whether the graph of each function is a parabola that opens upward or downward:ⓐ f(x)=−2x2−2x−3ⓑf(x)=5x2−2x−1

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Solve for f (x) = −2x2 − 2x − 3

Part (b) Step 1. Solve for f (x) = 5x2 − 2x − 1

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Logic and Functions

Theoretical and Mathematical Physics

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Determine whether the graph of each function is a parabola that opens upward or downward:
ⓐ $f (x) = - 2 x^{2} - 2 x - 3$
ⓑ $f (x) = 5 x^{2} - 2 x - 1$