This document defines quadratic equations as polynomial functions of degree 2, where the highest exponent is 2. It explains that a quadratic equation can be written in standard form as f(x) = ax^2 + bx + c, where a, b, and c are real numbers and a is not equal to 0. The graph of a quadratic equation is a parabola. Key features of a parabola include its axis of symmetry, which is the line that bisects the parabola, and its vertex, which is the highest or lowest point of the parabola. The document provides examples of finding the vertex and axis of symmetry of parabolas given their equations and of writing the equation of a parabola

1. 2.1 Quadratic
Equations
Essential Question:
How do you find maximum and minimum values of a
quadratic equation?
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2. Definition of a Polynomial Function
Let 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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3. Definition of Quadratic Function
a, b, and c are real numbers with a≠0
is called a quadratic equation.
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4. 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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5. Ex. 1) Graph the parabola. Identify the axis of symmetry
and vertex.
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6. Vertex of a Parabola
Given:
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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7. Rally Coach:
Find the vertex of each of the parabolas.
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10. 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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11. Ex. 3) Write the equation of a parabola whose vertex
is (-4, 11) and passes through the point (-6, 15).
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12. Assignment:
2.1 p. 134 #11, 19, 25,
27, 28, 41, 45, 47,
59, 61
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