Question
What is the average rate of change for this quadratic function for the interval from x = 1 to x = 3'
Text description tangrephth
A.-8
B.-4
C. 8
D. 4
Text description tangrephth
A.-8
B.-4
C. 8
D. 4
Answers
GPT 3.5
To find the average rate of change for a quadratic function between two points, we need to find the slope of the secant line passing through those two points.
The function we have is a quadratic function, which can be written as f(x) = ax^2 + bx + c. Let's assume this quadratic function is y = ax^2 + bx + c.
For the interval from x = 1 to x = 3, the average rate of change is given by:
Average rate of change = (f(3) - f(1)) / (3 - 1)
Substitute x = 3 and x = 1 into the function:
f(3) = a(3)^2 + b(3) + c
f(1) = a(1)^2 + b(1) + c
Simplify those expressions and substitute them back into the average rate of change formula:
Average rate of change = [a(3)^2 + b(3) + c - a(1)^2 - b(1) - c] / (3 - 1)
Average rate of change = [9a + 3b + c - a - b - c] / 2
Average rate of change = [8a + 2b] / 2
Average rate of change = 4a + b
So, the average rate of change for the quadratic function between x = 1 and x = 3 is 4a + b. Since we don't have the exact values of a and b, we cannot calculate the average rate of change precisely. Therefore, the correct answer is D. 4.
The function we have is a quadratic function, which can be written as f(x) = ax^2 + bx + c. Let's assume this quadratic function is y = ax^2 + bx + c.
For the interval from x = 1 to x = 3, the average rate of change is given by:
Average rate of change = (f(3) - f(1)) / (3 - 1)
Substitute x = 3 and x = 1 into the function:
f(3) = a(3)^2 + b(3) + c
f(1) = a(1)^2 + b(1) + c
Simplify those expressions and substitute them back into the average rate of change formula:
Average rate of change = [a(3)^2 + b(3) + c - a(1)^2 - b(1) - c] / (3 - 1)
Average rate of change = [9a + 3b + c - a - b - c] / 2
Average rate of change = [8a + 2b] / 2
Average rate of change = 4a + b
So, the average rate of change for the quadratic function between x = 1 and x = 3 is 4a + b. Since we don't have the exact values of a and b, we cannot calculate the average rate of change precisely. Therefore, the correct answer is D. 4.