Question

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 graph$f\left(x\right)=x^2+5$.

Short answer

The sentence, “The graph of the parent function is translated down to form the graph of $f\left(x\right)=x^2+5$” is false.

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

Step-by-step solution

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

A quadratic function, which is written in the form, $y=a{x}^2+bx+c$, where, $a\ne 0$is called the standard form of the quadratic function.

Step 2. Define vertical translation of the graph.

e graph $g\left(x\right)=x^2+c$is the graph $f\left(x\right)=x^2$ translated vertically.

If $c>0$, the graph $f\left(x\right)=x^2$is translated $\left|c\right|$units up.

If $c<0$, the graph of $f\left(x\right)=x^2$is translated $\left|c\right|$ units is down.

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

Observe the graph $f\left(x\right)=x^2+5$.

Here,$c=5$

So, the graph of the parent function is translated into 5 units up to form the graph role="math" localid="1647840467756" $f\left(x\right)=x^2+5$.

Therefore, the sentence, “The graph of the parent function is translated down to form the graph of $f\left(x\right)=x^2+5$” is false.

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