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I figured out the vertex and factored form of the equation. By doing this, I got the graph´s vertex, rate of change, axis of symmetry, and the x and y intercepts.

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Vertex: (x+6)^2-4
Factored: (x+8)(x+4)

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standard- y=x^2+8-9
vertex- y=(x-4)^2+7
xint- (0,9) (0,1)
yint- (-9,0)

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Standard Form: y=x^2-12x+20
Factored Form: (x+2)(x+10)
x-intercepts: -2, -10
y-intercepts: 20

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standard- y=x^2+8-9
vertex- y=(x-4)^2+7
xint- (0,9) (0,1)
yint- (-9,0)

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Click on it to expand
First change the equation to vertex form and then use the vertex and a value to graph

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Standard Form:y=x^2+4x-32
Factored Form: y=(x-4)(x+8)
x-intercepts: 4, -8
y-intercept: -32

-To get to Standard Form, we multiplied using the model and then added 16
-To get to Factored Form we guess and checked to find which numbers would get us 4x and -32.

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Vertex- y=(x-4)^2+
standard- y= x^2-8x+9
xint- (0,9) (0,-1)

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First you need to convert the equation to standard form and then to vertex form.
Standard: y=x^2 -8x+12
Vertex: y=(x-4)^2 -4
Then plot vertex and plug x values into the equation

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Vertex Form: (x-5)^2 -9
Factor Form: (x-2)(x-8)
x-intercepts: 2 and 8
y intercepts: -16

a. We found vertex form by dividing 10 by 2 and putting it in the parenthesis that are squared and subtract it by the amount needed to get from 25 (the squared value of 5) to 16
b. We found factor form by determining the different ways to get 16 that can create -10, which ended up being 2 and 8.
c. by doing the opposite from the two numbers in factor form
d. c in standard form

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Graphing

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Graphing

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Graphing

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Graphing

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Converting the Forms

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Converting the Forms

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Converting the Forms

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Converting the forms