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Chapter 9: Q. 478 (page 985)

Determine if the following parabolas open up or down.

a. y=-3x2+3x-1

b.y=5x2+6x+3

Short Answer

Expert verified

Part (a). The parabola opens downward.

Part (b). The parabola opens upward.

Step by step solution

01

Part (a). Step 1. Given information.

The given equation of a parabola isy=-3x2+3x-1.

02

Part (a).  Step 2. Use the property of the parabola.

The standard form of the parabola is y=ax2+bx+c.

If a>0, then the parabola opens upward.

If a<0, then the parabola opens downward.

In the given equation y=-3x2+3x-1, a=-3<0.

So, the parabola opens downward.

03

Part (b). Step 1. Given information.

The given equation of the parabola isy=5x2+6x+3.

04

Part (b). Step 2. Use the property of the parabola.

The standard form of the parabola is y=ax2+bx+c.

If a>0, the parabola opens upward.

If a<0, the parabola opens downward.

In the given equation y=5x2+6x+3, a=5>0.

So, the parabola opens upward.

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