November 25, 2014
1.8: Writing Standard Quadratic
Equations in Vertex Form…
otherwise known as completing
the square
November 25, 2014
Why?
• Graphing a quadratic in vertex form is easier than graphing a quadratic in standard form.
• Completing the square is another method to solve quadratics
• Other methods to solve quadratics:
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November 25, 2014
Review: What is vertex form?
November 25, 2014
Reasoning behind the madness:
to put a standard form equation in vertex form, it has to be a perfect trinomial
November 25, 2014
Examples of perfect square trinomials:
• x2 + 6x + 9 = y
• x2 ­ 10x + 25 = y
• x2 + 2x + 1 = y November 25, 2014
Why do these work? Factor them:
• x2 + 6x + 9 = y
• x2 ­ 10x + 25 = y
• x2 + 2x + 1 = y November 25, 2014
Creating a Perfect Square Trinomial
• In the following perfect square trinomial,
the constant term is missing.
• X2 + 14x + ____
• Find the constant term by halfing the #
with x and then squaring it
November 25, 2014
Perfect Square Trinomials
• Create perfect square trinomials.
• x2 + 20x + ___
• x2 - 4x + ___
• x2 + 5x + ___
100
4
25/4
November 25, 2014
Practice Completing the Square
Fill in the blanks to make the equation true.
a b
c 1) x2 + 8x + ______ = (x + 4)2
2) x2 + 16x + ______ = (x+8)2
3) x2 ­ 6x + ______ = (x ­ 3)2
4) How does the number in “b” compare to “c”?
5) How does the number in “c” compare to “a”?
6) If you are given “a”, is there more than one possibility for “b” or “c”?
November 25, 2014
More Practice
Complete the squares for the following:
7) x2 + 2x + ______ = (x + ______ )2
8) x2 + 10x +______ = (x + ______ )2
9) x2 ­ 5x + ______ = (x + ______ )2
10) x2 + 6x + ______ = (x + ______ )2
11) x2 + 7x + ______ = (x + ______ )2
12) x2 + 4 x +______ = (x + ______ )2
13) x2 ­ 18x + ______ = (x + ______ )2
November 25, 2014
Steps to complete the square when the trinomial is not perfect:
Note: The quadratic coefficient must be equal to 1 before you complete the square, so you must divide all terms by the quadratic coefficient if it is not already 1. • Replace the y with a 0
• Move the constant term to the right side of the equation.
• Find the term that completes the square on the left side of the equation. Add that term to both sides.
• Factor the trinomial
• Move constant to same side as trinomial and set = y
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Write the following in vertex form:
Write the following equation in vertex form by
completing the square:
Step 1: Move constant term to the right side of the
equation.
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Completing the Square-Example
#2
Write the following in
vertex form:
Step 1: Move constant
term to the right side of
the equation.
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November 25, 2014
Write the following in vertex form:
Try the following examples. Do your work on your
paper and then check your answers.
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