What is the graph of the function?
f(x) = 2x2
(1 point)
Responses
graphThe function has a minimum at the point left-parenthesis 0 comma 0 right-parenthesis and passes through the points left-parenthesis negative 1 comma 2 right-parenthesis and left-parenthesis 1 comma 2 right-parenthesis.
Image with alt text: graph The function has a minimum at the point left-parenthesis 0 comma 0 right-parenthesis and passes through the points left-parenthesis negative 1 comma 2 right-parenthesis and left-parenthesis 1 comma 2 right-parenthesis.
graphThe function has a minimum at the point left-parenthesis negative 2 comma 0 right-parenthesis and passes through the points left-parenthesis negative 3 comma 1 right-parenthesis and left-parenthesis negative 1 comma 1 right-parenthesis.
Image with alt text: graph The function has a minimum at the point left-parenthesis negative 2 comma 0 right-parenthesis and passes through the points left-parenthesis negative 3 comma 1 right-parenthesis and left-parenthesis negative 1 comma 1 right-parenthesis.
graphThe function has a minimum at the point left-parenthesis 0 comma 2 right-parenthesis and passes through the points left-parenthesis negative 1 comma 3 right-parenthesis and left-parenthesis 1 comma 3 right-parenthesis.
Image with alt text: graph The function has a minimum at the point left-parenthesis 0 comma 2 right-parenthesis and passes through the points left-parenthesis negative 1 comma 3 right-parenthesis and left-parenthesis 1 comma 3 right-parenthesis.
graphThe function has a minimum at the point left-parenthesis 0 comma 0 right-parenthesis and passes through the points left-parenthesis negative 2 comma 2 right-parenthesis and left-parenthesis 2 comma 2 right-parenthesis.
Image with alt text: graph The function has a minimum at the point left-parenthesis 0 comma 0 right-parenthesis and passes through the points left-parenthesis negative 2 comma 2 right-parenthesis and left-parenthesis 2 comma 2 right-parenthesis.
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The correct response is: "graphThe function has a minimum at the point left-parenthesis 0 comma 0 right-parenthesis and passes through the points left-parenthesis negative 1 comma 2 right-parenthesis and left-parenthesis 1 comma 2 right-parenthesis."
The correct answer is:
The graph of the function f(x) = 2x^2 has a minimum at the point (0, 0) and passes through the points (-1, 2) and (1, 2).
To graph the function f(x) = 2x^2, we can start by plotting some points on a coordinate plane.
We can choose different values of x and calculate the corresponding values of f(x).
Let's choose x = -2, -1, 0, 1, and 2:
For x = -2, f(x) = 2(-2)^2 = 8
For x = -1, f(x) = 2(-1)^2 = 2
For x = 0, f(x) = 2(0)^2 = 0
For x = 1, f(x) = 2(1)^2 = 2
For x = 2, f(x) = 2(2)^2 = 8
So the points we have are (-2, 8), (-1, 2), (0, 0), (1, 2), and (2, 8).
Plotting these points on the coordinate plane and connecting them, we will get a U-shaped curve opening upwards.
The minimum point of the graph is at (0, 0), where the curve reaches its lowest point. From there, the graph increases symmetrically on both sides.
I hope this explanation helps you understand how to graph the function f(x) = 2x^2.