Compare Linear, Exponential, and Quadratic Models

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Presentation transcript:

Compare Linear, Exponential, and Quadratic Models

Identifying from an equation: Linear y = mx + b Has an x with no exponent. y = 5x + 1 y = ½x 2x + 3y = 6 Quadratic y= ax2 + bx + c Has an x2 in the equation. y = 2x2 + 3x – 5 y = x2 + 9 x2 + 4y = 7 Exponential y = abx Has an x as the exponent. y = 3x + 1 y = 52x 4x + y = 13

LINEAR, QUADRATIC or EXPONENTIAL? y = 6x + 3 y = 7x2 +5x – 2 9x + 3 = y 42x = 8 Exponential Quadratic Linear Exponential

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

LINEAR, QUADRATIC or EXPONENTIAL? 5. 6. 7. 8. Exponential Quadratic Linear None of the above Ab. Value

Identifying from the Table Linear Y values don’t repeat Add or subtract same number on x & y Quadratic Y values repeat 2nd difference is the same Pattern with y values Exponential Y values don’t repeat. Common multiplication pattern

Identifying from the Table Linear -2 -1 1 4 7 2 10 Quadratic -2 -6 -1 -4 1 2 6 Exponential -2 0.08 -1 0.4 2 1 10 50 +3 +0 +2 +4 +6 +2 x5

LINEAR, QUADRATIC or EXPONENTIAL? 9. 10. x y -5 1 -4 2 -1 3 4 11 x y -2 -1 -4 -8 1 -16 3 -32 Quadratic Exponential

LINEAR, QUADRATIC or EXPONENTIAL? 11. 12. 13. x y 1 5 2 9 3 13 4 17 21 x y 1 2 -1 3 4 5 8 x y 1 3 2 9 27 4 81 5 243 Linear Quadratic Exponential

The table describes how a restaurants sales are changing over time. What type of function is represented by the data in the table? Predict the sales after 8 years? 14)

The table describes how a clothing stores sales are changing over time. What type of function is represented by the data in the table? Predict the sales after 10 years? 15)

The table describes the cost to operate a The table describes the cost to operate a freezer for a course of several months. What type of function is represented by the data in the table? Predict the cost after 5 months.