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Chapter 9: Q. 233 (page 944)

For each of the following exercises, determine if the parabola opens up or down.

(a)f(x)=-2x2-6x-7(b)f(x)=6x2+2x+3

Short Answer

Expert verified

The parabola of the function f(x)=-2x2-6x-7opens down.

The parabola of the functionf(x)=6x2+2x+3opens up.

Step by step solution

01

Part (a) Step 1. Given information

Given function is f(x)=-2x2-6x-7

We have to determine that the parabola is opens up or down.

02

Part (a) Step 2. Comparing the given function with the standard form

Compare f(x)=-2x2-6x-7with standard form role="math" localid="1645165935018" f(x)=ax2+bx+c.

We have, a=-2

Since the value of the leading coefficient ais negative, so the parabola opens down.

03

Part (b) Step 1. Given information

Given function isf(x)=6x2+2x+3

We have to determine that the parabola is opens up or down.

04

Part (b) Step 2. Comparing the given function with the standard form 

Compare f(x)=6x2+2x+3with the standard form f(x)=ax2+bx+c.

We have a=6

Since the value of the leading coefficient ais positive, so the parabola opens up.

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