6.1 graphing quadratic functions parabola axis of symmetry vertex
TRANSCRIPT
![Page 1: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/1.jpg)
6.1 Graphing Quadratic Functions
Parabola
Axis of symmetry
Vertex
![Page 2: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/2.jpg)
A Quadratic function
Parts of the Quadratic function.
CONSTANT TERM
0,2 awherecbxaxxf
termquadratic
termlinear
![Page 3: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/3.jpg)
The graph of a Quadratic function is called a parabola.
A Quadratic function
![Page 4: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/4.jpg)
Parabola are Symmetrical
Axis of Symmetry, splits it down the middle
![Page 5: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/5.jpg)
Parabola are Symmetrical
Points reflect across the axis of symmetry
5,4 5,0
2,3 2,1
![Page 6: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/6.jpg)
Parabola are Symmetrical
The equation for the axis symmetry is
5,4 5,0
2,3 2,1
a
bx
2
![Page 7: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/7.jpg)
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
![Page 8: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/8.jpg)
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
![Page 9: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/9.jpg)
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
![Page 10: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/10.jpg)
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
![Page 11: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/11.jpg)
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
![Page 12: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/12.jpg)
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
![Page 13: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/13.jpg)
How to graph the parabolaf(x) = 2- 4x + x2
Start a table using number higher and lower then 2, from the vertex. Plot points
![Page 14: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/14.jpg)
How to graph the parabolaf(x) = 2- 4x + x2
Connects the points.
![Page 15: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/15.jpg)
Graph the function. Show the y intercept, axis of symmetry and vertex
f(x) = -x2 + 2x + 3
![Page 16: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/16.jpg)
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?
![Page 17: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/17.jpg)
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)
![Page 18: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/18.jpg)
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
![Page 19: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/19.jpg)
Graph the function. Show the y intercept, axis of symmetry and vertex
f(x) = -x2 + 2x + 3
Plot the points
![Page 20: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/20.jpg)
Graph the function. Show the y intercept, axis of symmetry and vertex
f(x) = -x2 + 2x + 3
Connect the points
![Page 21: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/21.jpg)
Homework
Page 291
# 15, 19, 23, 25,
33 – 43 odd
![Page 22: 6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex](https://reader030.vdocuments.net/reader030/viewer/2022033011/56649f225503460f94c3a5e8/html5/thumbnails/22.jpg)
Homework
Page 291- 292
# 16, 22, 26,
32 - 42 even, 46, 47