Question

graph the function. \\( y(x) = 4x^2 - 6 \\) \
plot five points on the graph of the function: one point with \\( x = 0 \\), two points with negative \\( x \\)-values, and two points with positive \\( x \\)-values. then click on the graph-function button.

Explanation:

Step1: Find point at \( x = 0 \)

Substitute \( x = 0 \) into \( y = 4x^2 - 6 \).
\( y = 4(0)^2 - 6 = -6 \).
So the point is \( (0, -6) \).

Step2: Find points with negative \( x \)-values

Let \( x = -1 \):
\( y = 4(-1)^2 - 6 = 4 - 6 = -2 \).
Point: \( (-1, -2) \).

Let \( x = -2 \):
\( y = 4(-2)^2 - 6 = 16 - 6 = 10 \).
Point: \( (-2, 10) \).

Step3: Find points with positive \( x \)-values

Let \( x = 1 \):
\( y = 4(1)^2 - 6 = 4 - 6 = -2 \).
Point: \( (1, -2) \).

Let \( x = 2 \):
\( y = 4(2)^2 - 6 = 16 - 6 = 10 \).
Point: \( (2, 10) \).

Answer:

Points: \( (0, -6) \), \( (-1, -2) \), \( (-2, 10) \), \( (1, -2) \), \( (2, 10) \) (plot these on the graph).