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Intro to Polynomial Functions and quadratics.
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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