what ios the average rate of change for this quadratic function for the interval from x=0 to x=2
The parabola vertex is at the closed point (0, 1) on Y-axis. The left slope passes through the closed points at (minus 1, 0), (minus 2, minus 3), (minus 3, minus 8) and (minus 4, minus 15) in quadrant 3. The right slope passes through the closed points at (1, 0), (2, minus 3), (3, minus 8) and (4, minus 15) in quadrant 4.
To find the average rate of change for this quadratic function on the interval from x=0 to x=2, we need to calculate the slope of the line passing through the points (0, f(0)) and (2, f(2)), where f(x) represents the quadratic function.
Given that the vertex of the parabola is at (0, 1) and the function opens upwards, we can determine that the equation of the function is of the form f(x) = ax^2 + 1.
Plugging in the given points (0, 1) and (2, f(2)), we get the following system of equations:
1 = a(0)^2 + 1
f(2) = a(2)^2 + 1
1 = 1
f(2) = 4a + 1
Solving the second equation, we get:
f(2) = 4a + 1
f(2) = 4(1) + 1
f(2) = 5
Therefore, the point (2, 5) lies on the quadratic function.
Now, we can calculate the average rate of change as the slope of the line passing through (0, 1) and (2, 5) using the formula:
Average Rate of Change = (5 - 1) / (2 - 0)
Average Rate of Change = 4 / 2
Average Rate of Change = 2
So, the average rate of change for this quadratic function on the interval from x=0 to x=2 is 2.