Lesson 66
Mr. Jones
Algebra
Name________________________
Date:_______________
S.W. B. A. T: Identify quadratic functions and determine whether they have a
minimum or maximum. Graph quadratic functions and give the domain and
range.
DO NOW: Identify each of the following functions:
1) 2x + y = -6
2) y = │2x – 1│
3) y = 2x
4) y = 2x2
Definitions:
Quadratic function is any function written in the form f(x) = ax2 + bx + c or
y = ax2 + bx + c where a, b, and c are real numbers and a ≠ 0.
Examples:
Parabola is the graph of a quadratic function that is u-shaped or curved.
Vertex is the turning point of the parabola.
Minimum is the y-value of the vertex of a parabola that opens upwards.
Maximum is the y-value of the vertex of a parabola that opens downwards.
Example 1 Tell whether each function is quadratic. Explain
a)
y + 3x2 = -4
b) x2 + y = x2 – 3
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c) {(-4, 7), (-2, 5), (0, 1), (2, 2), (4, -7)}
d)
Exercise 1
a)
Tell whether each function is quadratic. Explain.
b)
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Example 2
1) If a > 0, the parabola of a quadratic function opens upward and the y-value of the
vertex of the function is the minimum value.
Example: y = 2x2 – 5
a = 2, the parabola has a minimum value and opens upward.
2) If a < 0, the parabola of a quadratic function opens downward and the y-value of the
vertex of the function is a maximum value.
Example: f(x) = -4x2
a= -4, the parabola has a maximum value and opens downward
Exercise 2
a) y = -3x2 + 6
b) -x2 + y = 2
Example 3
a)______________________
b)______________________
c)______________________domain
d)______________________range
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Exercise 3
a)______________________
b)______________________
c)______________________domain
d)______________________range
Example 4: Graph each quadratic function using a table of values.
a)
b)
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Exercise 4 Graph each quadratic function using a table of values.
a)
b)
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EXIT
Graph the following quadratic equation using a table of values:
y = -2x2 + 2
x
y=
(x, y)
-2
-1
0
1
2
a) Which direction does the parabola opens?
b) What is the vertex of the parabola?
c) Does the graph have a minimum or maximum value? What is the value?
d) What is the domain and range of the function?
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Lesson 66
Mr. Jones
Algebra
Name________________________
Date:_______________
Homework
Pages 594 -597 Section 9-1
Problems: 2, 4, 6, 8, 12, 14, 16, 18, 22, 24, 32, 34
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