• Slides: 21

Quadratic Equation Standard form: f(x) = ax 2 + bx + c

Finite Differences In a linear function, the finite differences are constant. In an exponential function, the finite differences are not constant, but they have a constant common ratio. For a quadratic function, the first finite differences are not constant. They do have a pattern in that they increase or decrease by the same number. The second finite differences are constant.

Examples What type function would best model the data set?

Examples Step 1: Determine whether or not the data represents a linear function Finite differences are not constant; not linear

Examples Step 2: Determine whether or not the data represents an exponential function. Ratios are not constant; not exponential

Examples Step 3: Determine whether or not the data represents a quadratic function. Second finite differences are constant; quadratic function

Examples Determine if the function rule for the set is linear, exponential, or quadratic.

Examples Determine if the function rule for the set is linear, exponential, or quadratic.

Writing Quadratic Functions You can use these three patterns to determine the quadratic function from the table of data. The value of c is the y-intercept (y when x = 0) The second difference is equal to 2 a The first difference between the y-values for x = 0 and x = 1 is equal to a + b

Examples Determine the function rule for the data set.

Examples Step 1: Determine the finite differences

Examples Step 2: Determine if the differences are constant

Examples Step 3: Determine whether or not the second finite differences are constant

Examples

Examples

Examples Determine the function rule for the set of data in the table.

Examples

Examples

Examples Write a quadratic function where the second finite difference is 4, the y-intercept is (0, 1), and a + b = 5

Examples Write a quadratic function where the second finite difference is 4, the y-intercept is (0, 1), and a + b = 5 The second finite difference is 4; 2 a = 4, so a = 2 a + b = 5, and a = 2, so b = 3; y-intercept = 1 = c f(x) = 2 x 2 + 3 x + 1