Pc 2.1 notes

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2.1 Quadratic EquationsEssential Question:How do you find maximum and minimum values of a quadratic equation?

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Definition of a Polynomial FunctionLet n be a nonnegative integer and let an, an-1, ... a1, a0 be real numbers

is called a polynomial function of x with degree n.

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Definition of Quadratic Functiona, b, and c are real numbers with a≠0

is called a quadratic equation.

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Graphs of Quadratics(AKA Parabolas)

- Axis of symmetry- Vertex- a is the __________________ and determines if parabola opens up (______) or down (______)

Standard Form: Axis of Symmetry:

Vertex:

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Ex. 1) Graph the parabola. Identify the axis of symmetry and vertex.

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Vertex of a ParabolaGiven:

The axis of symmetry for f(x) is:

The vertex of f(x) is:

Also, the vertex is a maximum if ___________

and a minimum if ___________

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Rally Coach:

Find the vertex of each of the parabolas.

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Ex. 2) The height y (in feet) of a ball thrown by a child is given by the equation below. a) What is the maximum height of the ball?b) How far is the ball thrown?

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Ex. 3) Write the equation of a parabola whose vertex is (-4, 11) and passes through the point (-6, 15).

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Assignment:

2.1 p. 134 #11, 19, 25, 27, 28, 41, 45, 47, 59, 61