The graph of the function y = x2x2 is shown below.
Which of the following shows the correct key features of the graph?
A)vertex (1/2, -21/4), axis of symmetry x=1/2 intercepts at (-1, 0) and (2, 0), y-intercept at (-2, 0).
B)vertex(1/2, -2 1/4), axis of symmetry x =-2 1/4, x-intercepts at (-1, 0) and (-2, 0), y-intercept at (0, 2).
C)vertex (1/2, -2 1/4), axis of symmetry x = -2 1/4, x-intercepts at (-1, 0) and (2, 0), y -intercept at (0, -2).
D)vertex (1/2, -2 1/4), axis of symmetry x=1/2, x-intercepts at (-1, 0) and (2, 0), y -intercept at (0, -2).
Explain your answer
The correct answer is C) vertex (1/2, -2 1/4), axis of symmetry x = -2 1/4, x-intercepts at (-1, 0) and (2, 0), y-intercept at (0, -2).
This is because the vertex of the graph of the function y = x^2 is at (1/2, -1/4). When we multiply this function by x^2, the y-coordinate of the vertex is multiplied by x^2 as well, resulting in the vertex of the new function being (1/2, -2 1/4).
The axis of symmetry for the graph of the function y = x^2 is x = 1/2. This axis of symmetry remains the same when we multiply the function by x^2, resulting in x = 1/2.
The x-intercepts for the function y = x^2 are at (-1, 0) and (1, 0). When we multiply the function by x^2, the x-intercepts remain the same.
The y-intercept for the function y = x^2 is at (0, 0). When we multiply the function by x^2, the y-intercept will be at (0, -2), as the output is multiplied by x^2.
Therefore, the correct key features of the graph of y = x^2x^2 are vertex (1/2, -2 1/4), axis of symmetry x = -2 1/4, x-intercepts at (-1, 0) and (2, 0), y-intercept at (0, -2).