Average Rate of Change of Quadratic Functions

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What is the average rate of change of a function over an interval?

Back

The average rate of change of a function over an interval [a, b] is given by the formula: (f(b) - f(a)) / (b - a). It represents the change in the function's value divided by the change in the input value.

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CCSS.HSF.IF.B.6

CCSS.8.F.B.4

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How do you find the average rate of change for g(x) = -x^2 + 4x - 1 over [2, 5]?

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1. Calculate g(5) = -5^2 + 4(5) - 1 = 4. 2. Calculate g(2) = -2^2 + 4(2) - 1 = 5. 3. Average rate of change = (4 - 5) / (5 - 2) = -1/3.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the average rate of change of n(x) = 4x^2 - 2x + 1 over [-1, 3]?

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1. Calculate n(3) = 4(3)^2 - 2(3) + 1 = 31. 2. Calculate n(-1) = 4(-1)^2 - 2(-1) + 1 = 7. 3. Average rate of change = (31 - 7) / (3 - (-1)) = 6.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

Determine the average rate of change of p(x) = -x^2 + 3x - 2 over [1, 4].

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1. Calculate p(4) = -4^2 + 3(4) - 2 = 2. 2. Calculate p(1) = -1^2 + 3(1) - 2 = 0. 3. Average rate of change = (2 - 0) / (4 - 1) = 2/3.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the average rate of change of h(x) = 3x^2 + 2x - 7 over [-2, 2]?

Back

1. Calculate h(2) = 3(2)^2 + 2(2) - 7 = 5. 2. Calculate h(-2) = 3(-2)^2 + 2(-2) - 7 = 1. 3. Average rate of change = (5 - 1) / (2 - (-2)) = 1.

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CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

Calculate the average rate of change of f(x) = 2x^2 - 3x + 5 over [1, 3].

Back

1. Calculate f(3) = 2(3)^2 - 3(3) + 5 = 8. 2. Calculate f(1) = 2(1)^2 - 3(1) + 5 = 4. 3. Average rate of change = (8 - 4) / (3 - 1) = 2.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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What is a quadratic function?

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A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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What does the graph of a quadratic function look like?

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The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

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CCSS.HSF-IF.C.7A

Front

What is the vertex of a quadratic function?

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The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction the parabola opens. It can be found using the formula (-b/2a, f(-b/2a)).

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What is the significance of the average rate of change in real-world applications?

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The average rate of change can represent various real-world scenarios, such as speed, growth rates, and changes in quantity over time.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6