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.
𝑦+20=𝑥2+8𝑥
Completing the Square with Parabolas
Step 2: Find
𝑏2=
82=4
𝑦+20=𝑥2+8𝑥
Completing the Square with Parabolas
Step 3: Take 𝑏
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.
−36 −36
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.
𝑦−1=𝑥2−4 𝑥
Completing the Square with Parabolas
Step 2: Find
𝑏2=
−42 =−2
𝑦−1=𝑥2−4 𝑥
Completing the Square with Parabolas
Step 3: Take 𝑏
2=−42 =−2 (−2)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.
−3 −3
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.
𝑥−25=𝑦2+12 𝑦
Completing the Square with Parabolas
Step 2: Find
𝑏2=
122 =6
𝑥−25=𝑦2+12 𝑦
Completing the Square with Parabolas
Step 3: Take 𝑏
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.
−11 −11
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.
𝑦=4 𝑥2−24 𝑥−5
𝑦+5=4 𝑥2−24 𝑥
+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 . 𝑏
2=−62 =−3
Completing the Square with Parabolas
Step 3: Take 𝑏
2=−62 =−3
Completing the Square with Parabolas
Step 4: Add to both
sides of the equation.
+36 +9¿
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.
−41 −41
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?