polynomial functions exponents- coefficients- degree- leading coefficient-
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2.1-LINEAR & QUADRATIC FUNCTIONS WITH MODELING
Polynomial FunctionsExponents-Coefficients-
Degree-
Leading Coefficient-
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Constant Function- Linear Function- Quadratic Function-
Ex) Write an equation for the linear function f such that f(3)=4 and f(-2)=-1.
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Quadratic FunctionsEx) Graph (sketch) f(x)=(x–3)2+5
Vertex:
Opens:
Axis of Symmetry
Equation of a Quadratic Function in Vertex Form
f(x)=a(x-h)2+k
Vertex: Axis of Symmetry:
a:
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Ex) Find the vertex, axis of symmetry, and determine which direction the parabola opens.
a) f(x)=-(x+2)2-4 b) g(x)=3x2
Equation of a Quadratic Function in Standard Form
f(x)=ax2+bx+c a
bh
2
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Ex) Find the vertex and axis of symmetry of the parabola.f(x)=3x2+6x+7
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If asked to describe a quadratic function/graph, use the following words:Vertex, axis of symmetry, opens,
stretch/shrink, even, x-intercept, y-intercept, etc.
Ex) Write a quadratic function given a vertex (1, 5) and point (4, 8).
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LINEAR & QUADRATIC MODELING Linear Correlation
StrengthDirection
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Examples of Linear Modeling Word ProblemsConstant rate of change (slope)Depreciation
Examples of Quadratic Modeling Word Problems2 things changingArea of rectangle, free fall motion, min/max
value
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Ex) A car depreciated to $17,000 after 3 years. If the initial cost was $25,000, what was the value for the 6th year? Write an equation to model this problem and find the answer.
*If the question says that something depreciates and doesn’t give a value it depreciated to, that means it depreciated to $0.
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Projectile Motion/Free Fall Motion
002
2
1)( stvgtts
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Ex) Jill threw a ball in the air from a height of 4 ft with initial velocity 20 ft/sec.a) Write the function.
b) What’s the maximum height of the ball?
c) How long does it take to get to the max. height?
d) When is it at 9 ft?
e) After how long does the ball hit the ground?
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Ex) T.F. South sells cans of pop in vending machines. They find that sales average 10,000 cans per month when the cans are $0.50 each. For each nickel increase in price, the sales per month drop by 500 cans.
a) Determine a function R(x) for total revenue where x is the number of $0.05 increases in price.
b) How much should TFS charge per can for maximum revenue?