Quadratic Equations - Algebra - Lecture Notes, Study notes of Algebra

Quadratic Equations, Vertex and Axis, Symmetry, Graph of the Function, Domain, Range of the Function, Function is Increasing, Decreasing, Without Graphing, Maximum Value are the key points of this lecture.

Typology: Study notes

2011/2012

Uploaded on 12/31/2012

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Lesson
Quadratic Functions
Find the vertex and axis of s
y
mmetr
y
of the
g
raph of the function.
1) f(x) = x2 + 8x
2) f(x) = x2 + 6x + 8
3) f(x) = -7x2 - 14x - 3
4) f(x) = -10x2 - 2x - 3
Graph the function usin
g
its vertex, axis of s
y
mmetr
y
, and intercepts.
5) f(x) = x2 - 6x
x
-10 -5 5 10
y
40
20
-20
-40
x
-10 -5 5 10
y
40
20
-20
-40
6) f(x) = x2 - 4x + 4
x
-10 -5 5 10
y
40
20
-20
-40
x
-10 -5 5 10
y
40
20
-20
-40
CollegeAlgebra
pf3
pf4

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Lesson

Quadratic Functions

Find the vertex and axis of symmetry of the graph of the function.

1) f(x) = x2 + 8x

2) f(x) = x2 + 6x + 8

3) f(x) = -7x2 - 14x - 3

4) f(x) = -10x2 - 2x - 3

Graph the function using its vertex, axis of symmetry, and intercepts.

5) f(x) = x2 - 6x

-10 -5 5 10 x

y 40

20

-10 -5 5 10 x

y 40

20

6) f(x) = x2 - 4x + 4

-10 -5 5 10 x

y 40

20

-10 -5 5 10 x

y 40

20

7) f(x) = x2 + 4x - 5

-10 -5 5 10 x

y 10

5

-10 -5 5 10 x

y 10

5

8) f(x) = -x2 - 6x - 8

-10 -5 5 10 x

y 10

5

-10 -5 5 10 x

y 10

5

9) f(x) = 2x2 + 20x + 51

-10 -5 5 10 x

y 10

5

-10 -5 5 10 x

y 10

5

Determine the domain and the range of the function.

10) f(x) = x2 + 8x

Answer Key

Testname: 12_QUADRATIC EQUATIONS

  1. (-4, - 16); x = - 4
  2. (-3, - 1); x = - 3
  3. (-1, 4) ; x = - 1
    • 1 10

; x = - 1 10

  1. vertex (3, - 9) intercepts (0, 0), (6, 0)

-10 -5 5 10 x

y 40

20

-10 -5 5 10 x

y 40

20

  1. vertex (2, 0) intercepts (0, 4), (2, 0)

-10 -5 5 10 x

y 40

20

-10 -5 5 10 x

y 40

20

  1. vertex (-2, - 9) intercepts (1, 0), (- 5, 0), (0, - 5)

-10 -5 5 10 x

y 10

5

-10 -5 5 10 x

y 10

5

  1. vertex (-3, 1) intercepts (-2, 0), (- 4, 0), (0, - 8)

-10 -5 5 10 x

y 10

5

-10 -5 5 10 x

y 10

5

  1. vertex (-5, 1) intercept (0, 51)

-10 -5 5 10 x

y 10

5

-10 -5 5 10 x

y 10

5

  1. domain: all real numbers range: {y|y ≥ - 16}

  2. domain: all real numbers range: {y|y ≥ 0}

  3. domain: all real numbers range: {y|y ≤ 9}

  4. increasing on (-6, ∞) decreasing on (-∞, - 6)

  5. increasing on (4, ∞) decreasing on (-∞, 4)

  6. increasing on (-∞, 3) decreasing on (3, ∞)

  7. minimum; 2

  8. minimum; 0

  9. minimum; - (^374)

  10. maximum; 1 2

  11. $

  12. 59 ft by 59 ft