Question

A quadratic function models the graph of a parabola. The quadratic functions, y = x2 and y = x2 + 3, are modeled in the graphs of the parabolas shown below.

Determine which situations best represent the scenario shown in the graph of the quadratic functions, y = x2 and y = x2 + 3. Select all that apply ( MULTIPLE CHOICE!! )

A) From x = -2 to x = 0, the average rate of change for both functions is negative.
B) For the quadratic function, y = x2, the coordinate (2, 3) is a solution to the equation of the function.
C) The quadratic function, y = x2 + 3, has an x-intercept at the origin.
D) The quadratic function, y = x2, has an x-intercept at the origin.
E) From x = -2 to x = 0, the average rate of change for both functions is positive.
D) For the quadratic function, y = x2 + 3, the coordinate (2, 7) is a solution to the equation of the function.

Answer 1

A, D, F

Explanation:

A) It is seen from the graph that the average rate of change from x=-2 to x=0 is negative since the values of y are decreasing (Correct answer)

B) The coordinate (2, 3) doesn't satisfy the function y=x^2 since 2^2isn't equal to 3 (Wrong answer)

C) The x intercept is the point where the line crosses the x axis. The coordinates of the origin is (0, 0). But the function y = x^2+3 doesn't have any x-intercept (Wrong answer)

D) For the function y=x^2, when the value of x is equal to 0, the value of y is also equal to 0 so the graph of the function has an x-intercept at the origin (Correct answer)

E) The average rate of change in the given interval is negatiove. Refer to the option A (Wrong answer)

F) The coordinate (2, 7) satisfies the function y=x^2+3 (2^2+3=7) so it is a solution to the equation of the function (Correct answer)