A quadratic equation can be written in three different forms: form, form, and form. In order to...
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![Page 1: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/1.jpg)
9.4 Graphing Quadratics
Three Forms
![Page 2: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/2.jpg)
A quadratic equation can be written in three different forms: form,
form, and form.
In order to graph each form, we need four key points and a key axis. The method to find these varies by form.
vertex axis of symmetry x-intercepts y-intercept
vertexstandardfactored
![Page 3: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/3.jpg)
The vertex form of a quadratic equation is:
The graph the function is a parabola with vertex at . The parabola is symmetric with respect to the line
. If , the parabola opens ; if
, the parabola opens .
Vertex Form
f x a x h 2 k
h,k
x h a 0a 0upward
downward
![Page 4: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/4.jpg)
1.
a. Find the vertex.
b. Find the axis of symmetry.
c. Find the x-intercepts (let y=0)
d. Find the y-intercept (let x=0)
Graph the parabola.
f x 2 x 3 2 8
![Page 5: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/5.jpg)
![Page 6: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/6.jpg)
2.
a. Find the vertex.
b. Find the axis of symmetry.
c. Find the x-intercepts (let y=0)
d. Find the y-intercept (let x=0)
Graph the parabola.
f x x 3 2 1
![Page 7: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/7.jpg)
![Page 8: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/8.jpg)
The vertex form of a quadratic equation is:
The graph the function is a parabola with
vertex at . The parabola is symmetric with respect to the line
. If , the parabola opens ; if , the parabola opens .
Standard Form
b
2a, f
b
2a
x b
2a a 0a 0upward
downward
f x ax2 bx c
![Page 9: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/9.jpg)
3.
a. Find the vertex.
b. Find the axis of symmetry.
c. Find the x-intercepts (let y=0)
d. Find the y-intercept (let x=0)
Graph the parabola.
f x x2 2x 1
![Page 10: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/10.jpg)
![Page 11: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/11.jpg)
4.
a. Find the vertex.
b. Find the axis of symmetry.
c. Find the x-intercepts (let y=0)
d. Find the y-intercept (let x=0)
Graph the parabola.f x 2x2 7x 4
![Page 12: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/12.jpg)
![Page 13: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/13.jpg)
The vertex form of a quadratic equation is:
The graph the function is a parabola with
vertex at . The parabola is symmetric with respect to the line
. If , the parabola opens ; if , the parabola opens .
Factored Form
r1 r22, f
r1 r22
x r1 r22 a 0
a 0upwarddownward
f x a x r1 x r2
![Page 14: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/14.jpg)
5.
a. Find the vertex.
b. Find the axis of symmetry.
c. Find the x-intercepts (let y=0)
d. Find the y-intercept (let x=0)
Graph the parabola.
f x 12x 1 x 5
![Page 15: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/15.jpg)
![Page 16: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/16.jpg)
6.
a. Find the vertex.
b. Find the axis of symmetry.
c. Find the x-intercepts (let y=0)
d. Find the y-intercept (let x=0)
Graph the parabola.
f x x 3 x 2
![Page 17: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/17.jpg)
![Page 18: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/18.jpg)
7. The parabola has a vertex at and passes through the point
Write the equation in vertex form.
2, 5 3,0
![Page 19: A quadratic equation can be written in three different forms: form, form, and form. In order to graph each form, we need four key points and a key.](https://reader035.fdocuments.in/reader035/viewer/2022071807/56649ebf5503460f94bca4b6/html5/thumbnails/19.jpg)
8. The parabola has a = 2, had x = -3 as its axis of symmetry, and passes through the point
Write the equation in vertex form.
3, 8