Standard Form Of A Quadratic Page 3
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1
2
3But WHY does the Quadratic Formula give solutions to a quadratic equation in standard form? Don’t
you want to know??? Hopefully you noticed that if a quadratic is in vertex form (like the last example
on the previous page) you can easily solve the quadratic equation by isolating the square then taking
the square root of both sides (note: square & square root are called INVERSE OPERATIONS because
they “undo” one another). So…with a partner fill in the blanks to derive the quadratic formula
yourselves. Take time to make sure you understand why you can do each step:
2
Given:
ax
+ bx + c = 0
2
Step 1:
a ( x
+ _______ x ) + c = 0
2
Step 2:
a ( x
+ _____ x + ______ ) + c - a*(_________) = 0
2
Step 3:
a( x + ________ )
+ ____________
= 0
2
Step 4:
a ( x + _______ )
=
____________
2
Step 5:
( x + _________ )
=
________________
Step 6:
x + _________
=
± _______________
Step 7:
x
=
__________________________
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