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Another new concept is going through different forms of equations to solve a problem. If a question asks you to solve a problem, but it isn't in the right form, you might have to go through 2 forms before you can solve in the right form.

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2x^2+11x+12
(2x+3)(x+4)
The 2x multiplies by the 4 making it 8x. (multiply your innards and outers) You then add the 8x and the 3x to get the 11x. This makes the numbers add the middle number. To get the third you number you just multiply the 3 and the 4. This gives you the 12.

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A new concept that we learned in this module is that, to fix a non-perfect square to make it perfect, you just have to add the value to make it perfect and subtract it. You need to subtract it to balance it out because you can't just randomly add in numbers.

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https://www.youtube.com/watch?v=ocxUbjOgfTs
This video explains how to complete the square to make it perfect. It shows how to take an equation from standard for to vertex form

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y=x^2+8x-13
y=x^2+8x+16-13-16
y=(x+4)^2-29
(8/2)^2=16

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f(x)=(x+d)(x+e)
Factored form is used when dealing with perfect squares. To get to standard form from factored form, you multiply . The numbers should add up the middle number in standard form and multiply to the third one.

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f(x)=ax^2+bx+c
To get from standard form to Vertex form you must complete the square

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if its not a perfect square then you can add the value that makes it perfect and subtract to fix the equation

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Take your dimension number, double it to get the middle number and square the dimension number to get the third number

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y=a(x-h)^2+k
Vertex: (h,k) (the sign becomes opposite for h)
Axis of Symm: x=h
Solving for a: pick an x&y besides the vertex and plug it in

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The purpose of h is to shift left and right

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the purpose of k is to move the vertex up and down the y axis

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The lowest or highest point

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A line that shows the middle of the parabola (you could fold one half onto the other perfectly

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The point where the parabola begins to curve (highest or lowest point of the parabola)