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General Solution to Quadratics by 
Completing the Square
(building the quadratic formula)
Solve for x by completing the square
ax2
 + bx +c = 0
2
3
If you remember from our quadratics unit, we can 
find the x value at the vertex, and the axis of 
symmetry by 
h = 
The quadratic formula can be represented by two 
fractions.
The first part is the h value.
The second part is the horizontal distance from the 
axis of symmetry to the x intercepts in both the 
positive
 and negative direction.
4
5
Ex. Sove   x2 
+ 3x ­ 9 = 0
6

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