Question

this table represents a quadratic function with a vertex at (1,0). what is the average rate of change for the interval from x = 5 to x = 6? a. 25 b. 7 c. 9 d. 5

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 5\), \(b=6\). First, find the pattern of the function. Since the vertex is at \((1,0)\), the quadratic function is \(y=(x - 1)^2\).

Step2: Calculate \(f(5)\) and \(f(6)\)

When \(x = 5\), \(y=(5 - 1)^2=16\). When \(x = 6\), \(y=(6 - 1)^2=25\).

Step3: Apply the average - rate - of - change formula

Substitute into the formula \(\frac{f(6)-f(5)}{6 - 5}=\frac{25-16}{6 - 5}\).

Answer:

\(9\) (Option C)