Question

graph the following equation by plotting points.

\\y = 3x^2 - 12\\

complete the ordered pairs in the table below.

x	(x,y)
-1
0
1

(simplify your answers. type ordered pairs.)

Explanation:

⚡ Using what you learned: evaluating functions

Step 1: Evaluate at \( x = -2 \)

Substitute \( x = -2 \) into the equation \( y = 3x^2 - 12 \):

$$ y = 3(-2)^2 - 12 = 3(4) - 12 = 12 - 12 = 0 $$

Ordered pair: \( (-2, 0) \)

Step 2: Evaluate at \( x = -1 \)

Substitute \( x = -1 \) into the equation:

$$ y = 3(-1)^2 - 12 = 3(1) - 12 = 3 - 12 = -9 $$

Ordered pair: \( (-1, -9) \)

Step 3: Evaluate at \( x = 0 \)

Substitute \( x = 0 \) into the equation:

$$ y = 3(0)^2 - 12 = 0 - 12 = -12 $$

Ordered pair: \( (0, -12) \)

Step 4: Evaluate at \( x = 1 \)

Substitute \( x = 1 \) into the equation:

$$ y = 3(1)^2 - 12 = 3(1) - 12 = 3 - 12 = -9 $$

Ordered pair: \( (1, -9) \)

Answer:

The completed ordered pairs for the table are:

• For \( x = -2 \): \( (-2, 0) \)
• For \( x = -1 \): \( (-1, -9) \)
• For \( x = 0 \): \( (0, -12) \)
• For \( x = 1 \): \( (1, -9) \)