Standard form to factored form
We can just factor it the way we learned, where the "c" is the product of the two factors and "b" is the sum of the two factors.
Let's try an example!
Change y=3x^2+4x+1
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Find factors of 3.
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They are 1 and 3.
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So our only possible terms are (x+___) (3x___).
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Find the factors of 1.
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The factor of 1 is 1.
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So we can place (x+1) (3x+1).
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Let's check
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x multiplied by 3x is 3x^2.
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x multiplied by 1 is 1x.
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1 multiplied by 3x is 3x.
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1 multiplied by 1 is 1.
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Collect like terms which are x+3x=4x.
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We end up with 3x^2+4x+1.
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So we are correct!
We have y=(x+1) (3x+1)
In this factored, we have the x-intercepts which are (-1,0) and (-0.33,0).
Axis of symmetry
Add these two x-intercepts, and divide them by 2.
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(-1-0.33)/2
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(-1.33)/2
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(-0.665)
Optimal value
Plug-in the axis of symmetry in the original equation.
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y=(-0.665+1) (3(-0.665)+1)
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y=(0.335) (-1.995+1)
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y=(0.335) (-0.995)
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y=(-0.33)
Vertex is (-0.665, -0.33)
Now we are ready to graph!
Try these...
1) y=x^2+11x+24
2) y=x^2-15x+56
3) y=x^2-x-90
Answers are...
1) y=(x+3) (x+8)
2) y=(x-7) (x-8)
3) y=(n-10) (n+9)
Video time
