Question

1. let $f(x) = 4x^2 + 2x + 1$ and let $g(x) = f(x + k)$. complete each statement. when $k = 2$, the graph of $g$ is the graph of $f$ translated \

$$\begin{choices} \\choice up \\choice down \\choice left \\choice right \\end{choices}$$

2 units. when $k = -3$, the graph of $g$ is the graph of $f$ translated \

$$\begin{choices} \\choice up \\choice down \\choice left \\choice right \\end{choices}$$

3 units. 6. leslie invests in a bank account that earns interest compounded quarterly. the expression $500(1.026)^{4t}$ can be used to find the account balance in $t$ years. part a what was leslie’s initial investment? $\boxed{}$ part b what is the quarterly interest rate the account earns? $\boxed{}$%

Explanation:

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Problem 5

Step1: Recall horizontal translation rule

For $g(x)=f(x+k)$, if $k>0$, shift left $k$ units; if $k<0$, shift right $|k|$ units.

Step2: Solve for $k=2$

Since $k=2>0$, graph shifts left 2 units.

Step3: Solve for $k=-3$

Since $k=-3<0$, graph shifts right 3 units.

Step1: Identify compound interest formula

The standard compound interest formula is $A=P(1+\frac{r}{n})^{nt}$, where $P$ = initial investment, $\frac{r}{n}$ = periodic rate.

Step2: Find initial investment (Part A)

Compare $500(1.026)^{4t}$ to the formula: $P=500$.

Step3: Find quarterly rate (Part B)

In $1+\frac{r}{n}=1.026$, the quarterly rate is $1.026-1=0.026$, or $2.6\%$.

Answer:

When $k=2$: left
When $k=-3$: right

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Problem 6