Multiple Choice What is the graph of the function? f(x) = 2x2
Without a specific graph provided, we cannot determine the exact shape of the graph for the function f(x) = 2x^2. However, we can provide some general information about the graph of this quadratic function.
The function f(x) = 2x^2 is a parabola that opens upwards because the coefficient of x^2 is positive (2 > 0). The graph will be symmetric with respect to the y-axis, meaning that the left side of the graph is a mirror image of the right side.
Additionally, the graph will intersect the y-axis at the point (0, 0) since f(0) = 2(0)^2 = 0. This is known as the vertex of the parabola.
It is also worth noting that as x approaches positive or negative infinity, the function will increase without bound. This is because the coefficient of x^2 is positive, causing the leading term to dominate as x gets larger in magnitude.
Without more specific instructions or information, it is not possible to determine the exact graph of f(x) = 2x^2.
The graph of the function f(x) = 2x^2 is a parabola.
To determine the graph of the function f(x) = 2x^2, we can use the concept of a quadratic function.
A quadratic function has the general form f(x) = ax^2 + bx + c, where a, b, and c are constants.
In this case, a = 2, b = 0 (since there is no x term), and c = 0.
Since b and c are both zero, the equation simplifies to f(x) = 2x^2.
To graph this function, we can start by plotting a few points and observing the pattern.
For example, let's substitute some values of x into the equation:
When x = -2, f(-2) = 2(-2)^2 = 2(4) = 8.
When x = -1, f(-1) = 2(-1)^2 = 2(1) = 2.
When x = 0, f(0) = 2(0)^2 = 2(0) = 0.
When x = 1, f(1) = 2(1)^2 = 2(1) = 2.
When x = 2, f(2) = 2(2)^2 = 2(4) = 8.
By plotting these points (-2, 8), (-1, 2), (0, 0), (1, 2), and (2, 8), we can see a pattern emerge. The graph is symmetric with respect to the y-axis and opens upward.
Therefore, the graph of the function f(x) = 2x^2 is a U-shaped curve called a parabola, with its vertex at the origin (0, 0).