10 8 Compare Linear Exponential and Quadratic Models

10. 8 Compare Linear, Exponential, and Quadratic Models • Students will Compare Linear, Exponential, and Quadratic Models

Identifying from an equation: Linear Quadratic Exponential Has an x with no exponent. Has an x 2 in the equation. Has an x as the exponent. y = 5 x + 1 y = ½x 2 x + 3 y = 6 y = 2 x 2 + 3 x – 5 y = x 2 + 9 x 2 + 4 y = 7 y = 3 x + 1 y = 52 x 4 x + y = 13

Examples: • LINEAR, QUADRATIC or EXPONENTIAL? a)y = 6 x + 3 b)y = 7 x 2 +5 x – 2 c)9 x + 3 = y d)42 x = 8

Identifying from a graph: Linear Quadratic Exponential Makes a straight line Makes a U or ∩ Rises or falls quickly in one direction

LINEAR, QUADRATIC or EXPONENTIAL? a) b) c) d)

Is the table linear, quadratic or exponential? Linear • Never see the same y value twice. • 1 st difference is the same Quadratic • See same y more than once. • 2 nd difference is the same Exponential • y changes more quickly than x. • Never see the same y value twice. • Common multiplication pattern

EXAMPLE 2 b. Identify functions using differences or ratios x – 2 – 1 0 1 2 y – 2 1 4 7 10 Differences: 3 3 ANSWER The table of values represents a linear function.

EXAMPLE 2 Identify functions using differences or ratios Use differences or ratios to tell whether the table of values represents a linear function, an exponential function, or a quadratic function. a. x y – 2 – 6 First differences: 0 Second differences: 2 – 1 – 6 0 – 4 2 1 0 4 2 2 6 6 2 ANSWER The table of values represents a quadratic function .

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. ANSWER x – 2 – 1 0 1 y 0. 08 0. 4 2 10 exponential function

x y 0 -5 -2 -2 1 -4 -1 -4 2 -1 0 -8 3 4 2 -32 4 11 5 -256

Is the table linear, quadratic or exponential? x y x y 1 5 1 0 1 3 2 9 2 -1 2 9 3 13 3 0 3 27 4 17 4 3 4 81 5 21 5 8 5 243

EXAMPLE 3 Write an equation for a function Tell whether the table of values represents a linear function, an exponential function, or a quadratic function. Then write an equation for the function. x – 2 – 1 0 1 2 y 2 0. 5 0 0. 5 2

EXAMPLE 3 Write an equation for a function SOLUTION STEP 1 Determine which type of function the table of values represents. x – 2 – 1 0 1 2 y 2 0. 5 0 0. 5 2 First differences: – 1. 5 Second differences: 1 – 0. 5 1 1. 5 1