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Chapter 9: Q. 479 (page 985)

Determine if the following parabolas open up or down.

a.y=x2+8x-1b.y=-4x2-7x+1

Short Answer

Expert verified

Part (a). Parabola opens upward.

Part (b). Parabola opens downward.

Step by step solution

01

Part (a). Step 1. Given information.

The given equation of the parabola isy=x2+8x-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, the parabola opens upward.

If a<0, the parabola opens downward.

In the given equation y=x2+8x-1, role="math" localid="1646287431881" a=1>0.

So, the parabola opens upward.

03

Part (b). Step 1. Given information.

The given equation isy=-4x2-7x+1.

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=-4x2-7x+1, role="math" localid="1646287676109" a=-4<0.

So, the parabola opens downward.

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