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.

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

Answer 1

Correct choices:
- From x = -2 to x = 0, the average rate of change for both functions is negative.
- y = x^2: (0 − 4)/(0 − (−2)) = −4/2 = −2
- y = x^2 + 3: (3 − 7)/2 = −4/2 = −2
- For y = x^2 + 3, (2, 7) is on the graph because 2^2 + 3 = 7.
- y = x^2 has an x-intercept at the origin because 0^2 = 0.

The other statements are false. (y = x^2 + 3 does not pass through the origin, and (2,3) is not on y = x^2.)