2.1-LINEAR & QUADRATIC FUNCTIONS WITH MODELING

Polynomial FunctionsExponents-Coefficients-

Degree-

Leading Coefficient-

Constant Function- Linear Function- Quadratic Function-

Ex) Write an equation for the linear function f such that f(3)=4 and f(-2)=-1.

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:

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

Ex) Find the vertex and axis of symmetry of the parabola.f(x)=3x2+6x+7

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).

LINEAR & QUADRATIC MODELING Linear Correlation

StrengthDirection

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

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.

Projectile Motion/Free Fall Motion

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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?

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?