Question

Using the function f(x)=1/4x^2and the values x = {-4-2, 0, 2, }, complete the table below

Answer 1

You have to determine the ordered pairs for given values of x of the function:

$f(x)=\frac{1}{4}(x)^2$

To do so, replace the function with each value of x and calculate the corresponding value of f(x):

1) For x=-4

-Replace the value in the formula

$\begin{gathered} f(x)=\frac{1}{4}(x)^2 \\ f(-4)=\frac{1}{4}(-4)^2 \end{gathered}$

-First solve the exponent

$f(-4)=\frac{1}{4}\cdot16$

-Then solve the multiplication

$f(-4)=4$

The first ordered pair is (-4,4)

2) For x=-2

-Replace the value in the formula

$\begin{gathered} f(x)=\frac{1}{4}(x)^2 \\ f(-2)=\frac{1}{4}(-2)^2 \end{gathered}$

-First solve the exponent

$f(-2)=\frac{1}{4}\cdot4$

-Then solve the multiplication

$f(-2)=1$

The second ordered pair is (-2,1)

3) For x=0

-Replace the value in the formula

$\begin{gathered} f(x)=\frac{1}{4}(x)^2 \\ f(0)=\frac{1}{4}(0)^2 \end{gathered}$

-First solve the exponent

$f(0)=\frac{1}{4}\cdot0$

-Then solve the multiplication

$f(0)=0$

The third ordered pair is (0,0)

4) Fox x=2

-Replace the value in the formula

$\begin{gathered} f(x)=\frac{1}{4}(x)^2 \\ f(2)=\frac{1}{4}(2)^2 \end{gathered}$

-First solve the exponent

$f(2)=\frac{1}{4}\cdot4$

-Then solve the multiplication

$f(2)=1$

The fourth ordered pair is (2,1)

5) For x=4

-Replace the value in the formula

$\begin{gathered} f(x)=\frac{1}{4}(x)^2 \\ f(4)=\frac{1}{4}(4)^2 \\ \end{gathered}$

-First solve the exponent

$f(4)=\frac{1}{4}\cdot16$

-Then solve the multiplication

$f(4)=4$

The fifth ordered pair is (4,4)