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To solve this problem, we changed the standard equation into vertex form, and used it to graph and plug in values.

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we put it into vertex form to help us graph and find x and y intercepts

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To get standard form we multiplied out the equation in vertex form to get y=x^2-6x-6x+36-16 which simplifies to y=x^2-12x+20.
To get factored form we looked at the standard form to see which two numbers when added together equal -12 and when multiplied together equal 20.
To get the x-intercepts we set y equal to 0 and solved.
To get the y-intercept we set x equal to 0 and solved.

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a. (2x-5)(x+4)
b. (3x-4)(x-6)
c. (3x-2)(x-2)
d. (7x+4)(x+7)

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Factored form:(x-8)(x-2)
x int: (8,0)(2,0)
y int:16

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To graph change it into vertex form y=(x+6)²-4

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For this problem, we went from factored form to standard form to vertex form.
standard: y= x^2+14x+45
vertex: y= (x+7)^2 -4

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Standard Form: y = x^2 - 8x - 9
Vertex From: y = (x - 4)^2 - 25
X-Intercepts: (9,0) and (-1,0)
Y-Intercept: (0,-9)

Explanation
To find Standard form, you have to simplify the factored form.

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

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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