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Chapter 9: Q10. (page 592)

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.

The graph of the parent function is translated down to form the graphfx=x2+5.

Short Answer

Expert verified

The sentence, 鈥淭he graph of the parent function is translated down to form the graph of fx=x2+5鈥� is false.

The correct replacement for the underlined term to make a true sentence is translated up.

Step by step solution

01

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, y=ax2+bx+c, where, a鈮�0is called the standard form of the quadratic function.

02

Step 2. Define vertical translation of the graph.

e graph gx=x2+cis the graph fx=x2 translated vertically.

If c>0, the graph fx=x2is translated cunits up.

If c<0, the graph of fx=x2is translated c units is down.

03

Step 3. Check whether the given sentence is true or false.

Observe the graph fx=x2+5.

Here,c=5

So, the graph of the parent function is translated into 5 units up to form the graph role="math" localid="1647840467756" fx=x2+5.

Therefore, the sentence, 鈥淭he graph of the parent function is translated down to form the graph of fx=x2+5鈥� is false.

The correct replacement for the underlined term to make a true sentence is translated up.

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