6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex
6.1 Graphing Quadratic Functions
Jan 05, 2016
6.1 Graphing Quadratic Functions. Parabola Axis of symmetry Vertex. A Quadratic function. Parts of the Quadratic function. CONSTANT TERM. A Quadratic function. The graph of a Quadratic function is called a parabola. Parabola are Symmetrical. Axis of Symmetry, splits it down the middle. - PowerPoint PPT Presentation
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6.1 Graphing Quadratic Functions
Parabola
Axis of symmetry
Vertex
A Quadratic function
Parts of the Quadratic function.
CONSTANT TERM
0,2 awherecbxaxxf
termquadratic
termlinear
The graph of a Quadratic function is called a parabola.
A Quadratic function
Parabola are Symmetrical
Axis of Symmetry, splits it down the middle
Parabola are Symmetrical
Points reflect across the axis of symmetry
5,4 5,0
2,3 2,1
Parabola are Symmetrical
The equation for the axis symmetry is
5,4 5,0
2,3 2,1
a
bx
2
The y – Intercept of a parabola
If x = 0, then c is the y intercept
0,)0()0(0 2 xwherecbaf
4)0(
4)0(6)0(3)0(
463)(
2
2
f
f
xxxf
The Vertex of the Parabola
The Vertex is a point at the highest or lowest point of the graph of a parabola. The Vertex is on the axis of symmetry, so its x coordinate is found by
a
bx
2
242)(
)(
2
2
xxxf
cbxaxxf
1)2(2
)4(
x
Now that you have x of the Vertex how do you find the y
x = 1 242)( 2 xxxf
0)1(
242)1(
2)1(4)1(2)1( 2
f
f
f
0,1
How can you tell if the Vertex is the highest or lowest point.
It all depends on “a”.
If a > 0, the parabola If a<0, the parabola is opens upward. opens downward
The Maximum or Minimum value is the y value of the vertex
If the vertex is ( -3, 1), of f(x)= x2 + 6x + 10, then the minimum value is 1. Since the
parabola is opening upward it is the minimum.
1,3
How to graph the parabolaf(x) = 2- 4x + x2
Rewrite the function. f(x) = x2 -4x + 2Find the y intercept: f(0) = 02 -4(0) + 2 = 2
(0, 2)
Find the vertex: a = 1, b= -4
2,22)2(
224)2()2(
2)1(2
)4(
2
f
f
x
How to graph the parabolaf(x) = 2- 4x + x2
Start a table using number higher and lower then 2, from the vertex. Plot points
How to graph the parabolaf(x) = 2- 4x + x2
Connects the points.
Graph the function. Show the y intercept, axis of symmetry and vertex
f(x) = -x2 + 2x + 3
Graph the function. Show the y intercept, axis of symmetry and vertex
f(x) = -x2 + 2x + 3
Does the graph open up or down?
What are a , b and c?
Graph the function. Show the y intercept, axis of symmetry and vertex
f(x) = -x2 + 2x + 3
Does the graph open up or down? Down
What are a , b and c?
a = -1
b = 2
c = 3, so the y intercept is (0,3)
Graph the function. Show the y intercept, axis of symmetry and vertex
f(x) = -x2 + 2x + 3
axis of symmetry is x = 1
What are a , b and c?
a = -1 The vertex is
b = 2
c = 3
4,14)1(
312)1()1(
1)1(2
)2(
2
f
f
x
Graph the function. Show the y intercept, axis of symmetry and vertex
f(x) = -x2 + 2x + 3
Plot the points
Graph the function. Show the y intercept, axis of symmetry and vertex
f(x) = -x2 + 2x + 3
Connect the points
Homework
Page 291
# 15, 19, 23, 25,
33 – 43 odd
Homework
Page 291- 292
# 16, 22, 26,
32 - 42 even, 46, 47
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