Question

x | f(x)
-2 | 3
-1 | -2
0 | -3
1 | 0
2 | 7
what is the rate of change for the interval between 0 and 2 for the quadratic equation as f(x) = 2x² + x - 3 represented in the table?
options: 1/5, 4, 5, 10

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) between two points \((x_1, f(x_1))\) and \((x_2, f(x_2))\) is given by \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\).

Step2: Identify the points

For the interval between \(x = 0\) and \(x = 2\), we have \(x_1=0\), \(f(x_1)=f(0)=- 3\) (from the table) and \(x_2 = 2\), \(f(x_2)=f(2)=7\) (from the table).

Step3: Calculate the rate of change

Substitute the values into the formula: \(\frac{f(2)-f(0)}{2 - 0}=\frac{7-(-3)}{2-0}=\frac{7 + 3}{2}=\frac{10}{2}=5\).

Answer:

5