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Big Ideas Lesson 8.6B 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 x2 in the equation. Has an x as the exponent. y = 5x + 1 y = ½x 2x + 3y = 6 y = 2x2 + 3x – 5 y = x2 + 9 x2 + 4y = 7 y = 3x + 1 y = 52x 4x + y = 13 Examples: • LINEAR, QUADRATIC or EXPONENTIAL? a)y = 6x + 3 b)y = 7x2 +5x – 2 c)9x + 3 = y d)42x = 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. • 1st difference is the same Quadratic • See same y more than once. • 2nd 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 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 2. for Examples 1 and 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 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 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 0.5 1 1.5 1