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Chapter 9: Q. 9.86 (page 924)

Determine whether the graph of each function is a parabola that opens upward or downward:

鈸� f(x)=鈭�2x2鈭�2x鈭�3

鈸�f(x)=5x2鈭�2x鈭�1

Short Answer

Expert verified
  • 鈸� The parabola will open downward for f(x)=鈭�2x2鈭�2x鈭�3
  • 鈸� The parabola will open upward forf(x)=5x2鈭�2x鈭�1

Step by step solution

01

Step 1. Given Information

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

鈸�f(x)=鈭�2x2鈭�2x鈭�3

鈸�f(x)=5x2鈭�2x鈭�1

We know that Parabola Orientation:

For the graph of the quadratic function f(x)=ax2+bx+c, if

  • a > 0, the parabola opens upwards.
  • a < 0, the parabola opens downwards.
02

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

Find the value of 鈥渁鈥�.

f(x)=ax2+bx+c

f(x)=鈭�2x2鈭�2x鈭�3

a=-2<0

Since the 鈥渁鈥� is negative, the parabola will open downward.

03

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

Find the value of 鈥渁鈥�.

f(x)=ax2+bx+c

role="math" localid="1646322415764" f(x)=5x2鈭�2x鈭�1a=5>0

Since the 鈥渁鈥� is positive, the parabola will open upward.

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