Relation between all three forms of quadratics
Vertex form
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Written as y=a(x-h)^2+k
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Vertex is the (h,k).
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Can be changed to standard form by expanding.
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Can be changed to factored form by finding the x-intercepts and writting it in factored form, or can be changed to standard form and then factored.
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To find x-intercepts, change y=0, and isolate x.
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The "h" value is the axis of symmetry.
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The "k" is the optimal value.
Useful site to test your knowledge-http://www.mathopenref.com/quadvertexexplorer.html
Standard form
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Written as y=ax^2+bx+c.
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Use the quadratic formula to find the x-intercepts.
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Can be changed to factored form by factoring if possible.
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Can be changed to vertex form by changing it into a perfect square.
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Axis of symmetry is the average of the x-intercepts.
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Optimal value can be found by pluging in the axis of symmetry (x) into the original equation.
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Vertex is the (axis of symmetry, optimal value).
Useful site for extra information-http://www.mathsisfun.com/algebra/standard-form.html
Factored form
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Written as y=a(x-r) (x-s).
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The "r" and "s" are the x-intercepts.
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Axis of symmetry is the average of the two x-intercepts.
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"x" can be found by setting each bracket equal to 0.
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Optimal value is found by substituting the axis of symmetry into the original equation.
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Vertex is (axis of symmetry, optimal value).
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Can be changed to vertex form by changing it into standard form first, and then changing it into vertex form.
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Can be changed to standard form by expanding.
Utilize this site to achieve information and examples-http://www.purplemath.com/modules/factquad.htm
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