Lesson 1: Key Features of Graphs of a Quadratic Function — Practice Questions

1. 1. What is the average rate of change of the function $f(x) = x^2$ over the interval $[2, 5]$? The average rate of change is ___.

2. 2. Calculate the average rate of change for the function $f(x) = 2x^2$ on the interval $[-3, 1]$. The average rate of change is ___.

3. 3. What is the average rate of change of the function $f(x) = -3x^2$ over the interval $[0, 2]$?

   • A. -6
   • B. 6
   • C. -12
   • D. -3

4. 4. Find the average rate of change of $f(x) = 5x^2$ over the interval $[-2, 2]$. The average rate of change is ___.

5. 5. Determine the average rate of change for the function $f(x) = -x^2$ on the interval $[-4, -1]$.

   • A. 5
   • B. -5
   • C. 15
   • D. -15

6. 6. For the function $f(x) = 4x^2$, which statement correctly describes its behavior?

   • A. Increasing on $(-\infty, 0)$ and decreasing on $(0, \infty)$
   • B. Decreasing on $(-\infty, 0)$ and increasing on $(0, \infty)$
   • C. Increasing on its entire domain.
   • D. Decreasing on its entire domain.

7. 7. On which interval is the function $g(x) = -\frac{3}{4}x^2$ decreasing?

   • A. $(-\infty, 0)$
   • B. $(0, \infty)$
   • C. $(-\infty, \infty)$
   • D. The function is never decreasing.

8. 8. If the function $f(x) = ax^2$ is decreasing on the interval $(0, \infty)$, what must be true about the coefficient $a$?

   • A. $a > 0$
   • B. $a < 0$
   • C. $a = 0$
   • D. $a$ can be any real number