L10.8 New

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#75 Objective Be able to compare, linear, quadratic, and exponential models Bell Ringer

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Choose functions using sets of ordered pairs EXAMPLE 1 Use a graph to tell whether the ordered pairs represent a linear function, an exponential function, or a quadratic function. a. SOLUTION

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Choose functions using sets of ordered pairs EXAMPLE 1

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Choose functions using sets of ordered pairs EXAMPLE 1

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Identify functions using differences or ratios EXAMPLE 2 Use differences or ratios to tell whether the table of values represents a linear function, an exponential function, or a quadratic function. First differences: 0 2 4 6 Second differences: 2 2 2 a.

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Identify functions using differences or ratios EXAMPLE 2 Differences: 3 3 3 3 b.

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GUIDED PRACTICE for Examples 1 and 2 First Difference 1 3 5 Second Difference 2 2

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GUIDED PRACTICE for Examples 1 and 2 2. Tell whether the table of values represents a linear function, an exponential function, or a quadratic function. First Difference .32 1.6 8 We notice there is no addition pattern to the differences, but we do see we can multiply the previous y by 5 to get the next y

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Write an equation for a function EXAMPLE 3 First differences: –1.5 –0.5 0.5 1.5 Second differences: 1 1 1 Tell whether the table of values represents a linear function, an exponential function, or a quadratic function. Then write an equation for the function. The table of values represents a quadratic function because the second differences are equal.

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Write an equation for a function EXAMPLE 3 Write an equation for the quadratic function. The equation has the form y = ax2. Find the value of a by using the coordinates of a point that lies on the graph, such as (1, 0.5). y = ax2 Write equation for quadratic function. 0.5 = a(1)2 Substitute 1 for x and 0.5 for y. 0.5 = a Solve for a. Cont.

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EXAMPLE 3 First Difference 2 2 2 2 Slope y-intercept Linear

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EXAMPLE 3 First Difference -6 -2 2 6 Second Difference 4 4 4 y = ax2 2 = a(1)2 2 = a Quadratic