Section4.7 Completing the Square

Ex1 Factor the following Perfect Square Trinomials. What is the relationship of b and c?

a)x2 + 18x + 81 / b) x2 – 16x + 64 / c)

Ex2 Find the value of c that makes each expression a perfect square trinomial.

1) x2 + 14x + c
a)______/ 2) x2 + 12x + c
b)______/ 3) m2 + 11m + c
c)______
Converting to Vertex Form by Completing the Square y= ax2 + bx + c
1. Move the constant to the other side (“y-side”).
2. The coefficient of the quadratic term must be 1. On the “x side” factor out a if it is something other than 1.
3. Create a perfect square trinomial.
{Just like finding c above}
4. Balance the equation. Careful if you have factored out a.
5. Factor and write as a binomial squared.
6. Isolate y or f(x)
& find vertex when needed / y = x2 - 6x + 7
y= -2x2 + 12x - 19

Ex3 Convert each of the following to vertex form & find vertex.

Together / You try
a) y = x2 + 22x + 8
Vertex:______/ b) y = x2 - 2x + 10
Vertex:______
a) y = 3x2- 9x + 5
Vertex:______/ b) y = 2x2 -16x + 28
Vertex:______

Ex4 Answer the following questions:

  • What do you want to remember about rewriting from standard to vertex form?
  • How can you check your answer?

Solving by Completing the Square ax2 + bx + c = 0
1. Check to see if the quadratic is already a perfect square, if so, go to step 6.
2. Move the constant to the other side.
3. The coefficient of the quadratic term must be 1. Reduce if possible. If not, factor out a on the “x side”.
4. Create a perfect square trinomial.
{Just like finding c above}
5. Balance the equation. Careful if you have factored out a.
6. Factor and write as a binomial squared.
7. Take the square root of each side (Don’t forget ±)
8. Solve for x and simplify (may need to rationalize) / x2 - 10x + 13 = 0
4x2+ 8x – 9 = 0

Ex5 Solve by completing the square. Together.

a) 3x2 - 36x + 150 = 0
a)______/ b) 4x2 + 12x + 9 = -3
b)______

Ex6 Solve by completing the square. You try.

a) x2 + 6x + 8 = 0
a)______/ b) 4x2 + 20x = – 1
b)______

Ex7 Answer the following question:

  • What do you want to remember about solving by completing the square?

Ex8 Solve the following word problems using completing the square.

a) The area of a triangle shown is 144 square units. What is the value of x?

2x
x + 10
A) -18
B) -18 or 8
C) 8
D) 16 / b) The height y (in feet) after t seconds of a ball that was thrown up in the air from the roof of a building is given by the function y = -16t2 + 64t + 50. What is the maximum height of the ball?
The maximum height of the ball is ____ ft.