Algebra 2 A Chapter 5 - Weebly

[Pages:5]Algebra 2 A Chapter 5

Section 1 Graphing Quadratic Functions

Graphs of Quadratic Functions ? The shape of a quadratic graph is called a parabola. ? The axis of symmetry is the line that divides a parabola into two mirror images.

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Graphs of Quadratic Functions ? The shape of a quadratic graph is called a

parabola. ? The axis of symmetry is the line that divides a parabola into two mirror images.

? The vertex of a parabola is the point where the parabola and the axis of symmetry meet. It is the minimum or maximum of the parabola. (It's the turning point.)

?Corresponding points are the mirror images of points

Quadratic functions y = ax2 + bx + c

1.) Look at a (leading coefficient of the quadratic):

If a is positive the parabola opens up

If a is negative the parabola opens down

2.) The axis of symmetry is at

x

b

2a

3.)The vertex is at

b 2a

,

yvertex

to find the y coordinate in the vertex

plug in (-b/2a) and solve for y

4.) y-intercept is at (0, c)

5.)Minimum or Maximum value occurs at the vertex. The min or max value is the y-coordinate of the vertex

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Example .....using algebra Find the y-intercept point, and the line of symmetry 1.) y = 3x2 + 6x ? 1

xb 2a

Y-int pt ( 0, -1) the c remember!

x (6) 1 2(3)

So x = -1 is the line of symmetry

2.) y = -3x2 ? 4x Y-int pt ( 0, 0)

So x = -2/3 is the line of symmetry

Example using the previous work

Also find the vertex 1.) y = 3x2 + 6x ? 1

Y-int pt ( 0, -1) x = -1 is the line of symmetry

Put the x of the line of symmetry ( also the x coordinate of the vertex) into the equation and find the y for the vertex

Vertex ( -1, -4)

2.) y = -3x2 ? 4x Y-int pt ( 0, 0)

x = -2/3 is the line of symmetry

Vertex ( -2/3, 4/3)

Vertex point:

b 2a , yvertex

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Make a table that includes the vertex

on your calculator!!!

ex 2.) y = -3x2 ? 4x Y-int pt ( 0, 0) x = -2/3 is the line of symmetry

Vertex ( -2/3, 4/3)

Knowing the line of symmetry give you a great place to start just scroll up and down the table and see the points. remember the vertex is on the line of symmetry so you only need to really scoll up OR down.

Using the calculator to find the vertex

Like pg 240 example b

On the graph will help you find the vertex as well try 2nd Calc max or min to help you find the vertex

QUADRATIC FUNCTIONS

Notice that the domain is all Real numbers while the Range depends on whether the function opens up or down.

Remember: The a in y = ax2 + bx + c will tell you if it opens up or down

If the function opens down (a < 0), then the range would start at the y coordinate for the vertex and get smaller.

While if the function opens up (a> 0), then the range would start at the y-coordinate of the vertex and go up from there.

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When you graph quadratics in my class. 1.) find the y-intercept 2.) find the axis of symmetry 3.) Find the vertex point. 4.) Make a table with the vertex being in the

middle of your table. 5.) use the points from the table to graph the function.

(use a minimum of 5 points: vertex, y-intercept, and the x-intercepts if the function has any)

In class example related to previous slide on the calculator y = x2 ? 2x + 1

1.) find the y-intercept 2.) find the axis of symmetry 3.) Find the vertex point. 4.) Make a table with the vertex being in the

middle of your table. 5.) use the points from the table to graph the function.

(use a minimum of 5 points: vertex, y-intercept, and the x-intercepts if the function has any.)

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