# Algebra unit 10.7

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09-Jul-2015Category

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### Transcript of Algebra unit 10.7

UNIT 10.7 LINEAR, QUADRATIC, AND EXPONENTIAL MODELS

A.7, 1B.2, 5C.1, 7D.no solutionSolve x2 6x 7 = 0 using the Quadratic Formula.

A.7, 4B.5, 6C.3, 5D.no solutionSolve y2 11y = 30 using the Quadratic Formula.

Solve 5z2 + 16z + 3 = 0 using the Quadratic Formula.

A.4, 3B.1C.2, 4D.no solutionSolve 4n2 = 19n 25 using the Quadratic Formula.

A.3B.2C.1D.noneWithout graphing, determine the number of x-intercepts of the graph of f(x) = 3x2 + x + 7.

A.9, 4B.4, 9C.2, 15D.15, 2Which are the solutions for 2x2 + 26x = 72?

You graphed linear, quadratic, and exponential functions. Identify linear, quadratic, and exponential functions from given data.

Write equations that model data.

Choose a Model Using GraphsA. Graph the ordered pairs. Determine whether the ordered pairs represent a linear, quadratic, or exponential function.(1, 2), (2, 5), (3, 6), (4, 5), (5, 2)Answer: The ordered pairs appear to represent a quadratic equation.

Choose a Model Using GraphsAnswer: The ordered pairs appear to represent an exponential function.

A.linearB.quadraticC.exponentialA. Graph the set of ordered pairs. Determine whether the ordered pairs represent a linear, quadratic, or exponential function. (2, 6), (0, 3), (2, 0), (4, 3)

A.linearB.quadraticC.exponentialB. Graph the set of ordered pairs. Determine whether the ordered pairs represent a linear, quadratic, or exponential function. (2, 0), (1, 3), (0, 4), (1, 3), (2, 0)

Choose a Model Using Differences or RatiosA. Look for a pattern in the table of values to determine which kind of model best describes the data.1 1 3 5 7First differences:Answer: Since the first differences are all equal, the table of values represents a linear function.

Choose a Model Using Differences or RatiosB. Look for a pattern in the table of values to determine which kind of model best describes the data.First differences:The first differences are not all equal. So, the table of values does not represent a linear function. Find the second differences and compare.

Choose a Model Using Differences or RatiosFirst differences:The second differences are not all equal. So, the table of values does not represent a quadratic function. Find the ratios of the y-values and compare.Second differences:Ratios:

Choose a Model Using Differences or RatiosThe ratios of successive y-values are equal. Answer: The table of values can be modeled by an exponential function.

A.linearB.quadraticC.exponentialD.none of the aboveA. Look for a pattern in the table of values to determine which kind of model best describes the data.

A.linearB.quadraticC.exponentialD.none of the aboveB. Look for a pattern in the table of values to determine which kind of model best describes the data.

Write an EquationDetermine which kind of model best describes the data. Then write an equation for the function that models the data.Step 1Determine which model fits the data.1 8 64 512 4096 First differences:

Write an EquationSecond differences:The table of values can be modeled by an exponential function.

Write an EquationStep 2Write an equation for the function that models the data.The equation has the form y = abx. Find the value of a by choosing one of the ordered pairs from the table of values. Lets use (1, 8).y= abxEquation for exponential function8= a(8)1x = 1, y = 8, b = 88= a(8)Simplify.1= aAn equation that models the data is y = (8)x.Answer: y = (8)x

A.quadratic; y = 3x2B.linear; y = 6xC.exponential; y = 3xD.linear; y = 3xDetermine which model best describes the data. Then write an equation for the function that models the data.

Example 4Write an Equation for a Real-World SituationKARATE The table shows the number of children enrolled in a beginners karate class for four consecutive years. Determine which model best represents the data. Then write a function that models that data.

Example 4Write an Equation for a Real-World SituationUnderstandWe need to find a model for the data, and then write a function.PlanFind a pattern using successive differences or ratios. Then use the general form of the equation to write a function.SolveThe first differences are all 3. A linear function of the form y = mx + b models the data.

Example 4Write an Equation for a Real-World Situationy= mx + bEquation for linear function8= 3(0) + bx = 0, y = 8, and m = 3b= 8Simplify.Answer:The equation that models the data is y = 3x + 8.CheckYou used (0, 8) to write the function. Verify that every other ordered pair satisfies the function.

Example 4A.linear; y = 4x + 4B.quadratic; y = 8x2C.exponential; y = 2 4xD.exponential; y = 4 2xWILDLIFE The table shows the growth of prairie dogs in a colony over the years. Determine which model best represents the data. Then write a function that models the data.

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