Completing the Square with Parabolas
Feb 22, 2016
Completing the Square with Parabolas
Perfect Square Trinomials
Examples x2 + 6x + 9 x2 - 10x + 25 x2 + 12x + 36
Creating a Perfect Square Trinomial
In the following perfect square trinomial, the constant term is missing. X2 + 14x + ____
Find the constant term by squaring half the coefficient of the linear term.
(14/2)2 X2 + 14x + 49
Perfect Square Trinomials
Create perfect square trinomials.
x2 + 20x + ___ x2 - 4x + ___ x2 + 5x + ___
100425/4
Completing the Square with Parabolas
Example 1: Put the following parabola in vertex form bycompleting the square:
Step 1: Move the constant, c, to the other side.
π¦+20=π₯2+8π₯
Completing the Square with Parabolas
Step 2: Find
π2=
82=4
π¦+20=π₯2+8π₯
Completing the Square with Parabolas
Step 3: Take π
2=82=4
Completing the Square with Parabolas
Step 4: Add to both
sides of the equation.
+16 +16
Completing the Square with Parabolas
Step 5: Factor the perfect square trinomial.
Completing the Square with Parabolas
Step 6: Move the
constant back to the right side.
β36 β36
Can you identify the vertex of this
parabola?
Completing the Square with Parabolas
Example 2: Put the following parabola in vertex form bycompleting the square:
Step 1: Move the constant, c, to the other side.
π¦β1=π₯2β4 π₯
Completing the Square with Parabolas
Step 2: Find
π2=
β42 =β2
π¦β1=π₯2β4 π₯
Completing the Square with Parabolas
Step 3: Take π
2=β42 =β2 (β2)2=4
Completing the Square with Parabolas
Step 4: Add to both
sides of the equation.
+4 +4
Completing the Square with Parabolas
Step 5: Factor the perfect square trinomial.
Completing the Square with Parabolas
Step 6: Move the
constant back to the right side.
β3 β3
Can you identify the vertex of this
parabola?
Completing the Square with Parabolas
Example 3: Put the following parabola in vertex form bycompleting the square:
Step 1: Move the constant, c, to the other side.
π₯β25=π¦2+12 π¦
Completing the Square with Parabolas
Step 2: Find
π2=
122 =6
π₯β25=π¦2+12 π¦
Completing the Square with Parabolas
Step 3: Take π
2=122 =6
Completing the Square with Parabolas
Step 4: Add to both
sides of the equation.
+36 +36
Completing the Square with Parabolas
Step 5: Factor the perfect square trinomial.
Completing the Square with Parabolas
Step 6: Move the
constant back to the right side.
β11 β11
Can you identify the vertex of this
parabola?
Completing the Square with Parabolas
Example 4: Put the following parabola in vertex form bycompleting the square:
Step 1: Move the constant, c, to the other side.
π¦=4 π₯2β24 π₯β5
π¦+5=4 π₯2β24 π₯
+5 +5
Completing the Square with Parabolas
Step 2: Find **In order to complete
the square, .**Before we can find ,
we must factor out the . π
2=β62 =β3
Completing the Square with Parabolas
Step 3: Take π
2=β62 =β3
Completing the Square with Parabolas
Step 4: Add to both
sides of the equation.
+36 +9ΒΏ
Completing the Square with Parabolas
Step 5: Factor the perfect square trinomial.
Completing the Square with Parabolas
Step 6: Move the
constant back to the right side.
β41 β41
Can you identify the vertex of this
parabola?
Completing the Square with Parabolas
You Try!Put the following
parabola in vertex form bycompleting the square:Can you identify the vertex of this
parabola?