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Chapter 9: Q. 235 (page 944)

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

(a)f(x)=-3x2+5x-1(b)f(x)=2x2-4x+5

Short Answer

Expert verified

The parabola of the function f(x)=-3x2+5x-1opens down.

The parabola of the function f(x)=2x2-4x+5opens up.

Step by step solution

01

Part (a) Step 1. Given information

Given function isf(x)=-3x2+5x-1

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)=-3x2+5x-1with the standard form f(x)=ax2+bx+c.

We have, a=-3

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)=2x2-4x+5

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)=2x2-4x+5with the standard form f(x)=ax2+bx+c

We have a=2

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

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