Question

graph the function.
$f(x) = -2x^2$
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-a-function button.

Explanation:

Step1: Choose x-values

Select \( x = -2, -1, 0, 1, 2 \) (two negative, one zero, two positive).

Step2: Calculate f(x) for x=-2

Substitute \( x = -2 \) into \( f(x) = -2x^2 \):
\( f(-2) = -2(-2)^2 = -2(4) = -8 \).
Point: \( (-2, -8) \).

Step3: Calculate f(x) for x=-1

Substitute \( x = -1 \):
\( f(-1) = -2(-1)^2 = -2(1) = -2 \).
Point: \( (-1, -2) \).

Step4: Calculate f(x) for x=0

Substitute \( x = 0 \):
\( f(0) = -2(0)^2 = 0 \).
Point: \( (0, 0) \).

Step5: Calculate f(x) for x=1

Substitute \( x = 1 \):
\( f(1) = -2(1)^2 = -2 \).
Point: \( (1, -2) \).

Step6: Calculate f(x) for x=2

Substitute \( x = 2 \):
\( f(2) = -2(2)^2 = -8 \).
Point: \( (2, -8) \).

Step7: Plot points

Plot \( (-2, -8) \), \( (-1, -2) \), \( (0, 0) \), \( (1, -2) \), \( (2, -8) \) on the graph. The parabola opens downward (since the coefficient of \( x^2 \) is negative) with vertex at \( (0, 0) \).

Answer:

The five points are \((-2, -8)\), \((-1, -2)\), \((0, 0)\), \((1, -2)\), \((2, -8)\). Plot these points and draw the downward - opening parabola through them.