Math 2 Honors
Name ___________________________
Lesson 3-6: Solving Quadratic Equations by Completing the Square
Learning Goals:
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I can complete the square of ax2+bx+c = 0 to write the quadratic in the form (x-p)2=q.
I can complete the square to rewrite a quadratic expression (ax2+bx+c) with the form a(x-h)2+k.
I can derive the quadratic formula by completing the square of ax2+bx+c = 0.
I can solve quadratic equations with real numbers as coefficients by completing the square.
1. Convert the following quadratic that is in vertex form to standard form:
y  3  4( x  2)2
Since we can change expressions in vertex form to standard, we should be able reverse the process and
change equations from standard form to vertex form. Write your factored form as a binomial squared
such as ( x  2)( x  2)  ( x  2)2 .
2. Factor the following:
a. x 2  12 x  36
b. x 2  22 x  121
c. x 2  34 x  289
3. How is each constant in the factored form related to the “b” value in the standard form?
4. How is each constant in the factored form related to the “c” value in the standard form?
5. Looking at the following expressions, what would have to be added so that the expression could
be factored into a binomial squared?
x 2  50 x  ___
x2  21x  ___
x 2  4 x  ___
6. Factor the above expressions: Write your factored form as a binomial squared.
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7. The following problems represent quadratic equations in standard form. Using what you have
learned so far, change the equations into vertex form. Keep in mind that if you add a number to
one side of an equation, you have to add it to the other side as well.
Vertex form y  a( x  h)2  k
y  x 2  12 x
y  x2  9x
y  x 2  15 x
8. Use the same process from number 7 to write the quadratic equations in vertex form.
(Hint: First move all constants to the side of the equation with “y”.)
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y  x 2  x  14
y  x 2  14 x  20
y  x 2  32 x  12
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9. Change the following into vertex form: (You must have an “a” value of 1, so start by dividing
through by your “a” value.)
y  3x 2  12 x  1
y  5x 2  4 x  3
y  6 x 2  7 x  13