Question

unction below, fill in the table of values, use the table to graph the function, and then identify the functions d
$y = 2x^2$

$x$	$x^2$	$y = 2x^2$
$-2$
$-1$
$0$
$1$
$2$
$3$

Explanation:

Step1: Calculate \( x^2 \) for \( x = -3 \)

To find \( x^2 \) when \( x = -3 \), we use the formula for squaring a number. Squaring a negative number gives a positive result, so \( (-3)^2 = (-3) \times (-3) = 9 \).

Step2: Calculate \( y = 2x^2 \) for \( x = -3 \)

Now that we know \( x^2 = 9 \) when \( x = -3 \), we substitute this value into the equation \( y = 2x^2 \). So, \( y = 2 \times 9 = 18 \).

We can continue this process for the other values of \( x \):

• For \( x = -2 \):
• Step1: \( (-2)^2 = (-2) \times (-2) = 4 \)
• Step2: \( y = 2 \times 4 = 8 \)
• For \( x = -1 \):
• Step1: \( (-1)^2 = (-1) \times (-1) = 1 \)
• Step2: \( y = 2 \times 1 = 2 \)
• For \( x = 0 \):
• Step1: \( 0^2 = 0 \times 0 = 0 \)
• Step2: \( y = 2 \times 0 = 0 \)
• For \( x = 1 \):
• Step1: \( 1^2 = 1 \times 1 = 1 \)
• Step2: \( y = 2 \times 1 = 2 \)
• For \( x = 2 \):
• Step1: \( 2^2 = 2 \times 2 = 4 \)
• Step2: \( y = 2 \times 4 = 8 \)
• For \( x = 3 \):
• Step1: \( 3^2 = 3 \times 3 = 9 \)
• Step2: \( y = 2 \times 9 = 18 \)

Answer:

For \( x = -3 \):

• \( x^2 = 9 \)
• \( y = 2x^2 = 18 \)

Completing the entire table:

\( x \)	\( x^2 \)	\( y = 2x^2 \)
-2	4	8
-1	1	2
0	0	0
1	1	2
2	4	8
3	9	18