Factored Form

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por DANIEL SHANG

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Vertex Form

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Expand and simplify

example

y = (x+3)(x-2)

y = x^2 - 2x + 3x - 6 y = x^2 + x - 6

Use FOIL (multiply firsts, outsides, insides and lasts)

Find vertex

Using the zeros, find AoS (x-value of vertex) with the formula: (r+s)/2 Zeros are the value of r and s but the opposite signs (if r was negative, the zero would be positive, if r was positive the zero would be negative. Same applies to value s) Substitute the AoS (for value x) in factored form to get K (y-value of vertex)

When you have the vertex and are writing the vertex form. The x-value (AoS) will be the opposite sign (if it is -, in the equation it will be +. If it is +, in the equation it will be -). The y-value stays the same. h = x-value of vertex and k = y-value of vertex

Example

y = (x-2)(x+6)

AoS = (r+s)/2 = (2-6)/2 = -4/2 =-2 Substitute -2 into factored form to get K

Y = 1(-2-2)(2+6) Y = 1(-4)(8) Y = -16 Vertex: (-2,-16)

y = (x+2)^2 - 16

Factored Form

Vertex Form

y= a(x-h)^2 + k

Standard Form

y = ax^2 + bx + c

y = a(x-r)(x-s)

A value is always the same in each form