section 4.6 – completing the square students will be able to: to solve equations by completing the...
TRANSCRIPT
Section 4.6 – Completing the Square
Students will be able to:
• To solve equations by completing the square
•To rewrite functions by completing the square
Lesson Vocabulary:
Completing the Square
Section 4.6 – Completing the Square
Section 4.6 – Completing the Square
Forming a square with model pieces provides a useful geometric image for completing the square
algebraically.
Essential Understanding:
Completing a perfect square trinomial allows you to factor the completed trinomial as the square of
a binomial.
Section 4.6 – Completing the Square
Problem 1:
What is the solution of each equation?
4x2 + 10 = 46
Section 4.6 – Completing the Square
Problem 1:
What is the solution of each equation?
3x2 – 5 = 25
Section 4.6 – Completing the Square
Problem 1:
What is the solution of each equation?
7x2 – 10 = 25
Section 4.6 – Completing the Square
Problem 1:
What is the solution of each equation?
2x2 + 9 = 13
Section 4.6 – Completing the Square
Problem 2:While designing a house, an architect used windows like the one
shown here. What are the dimensions of the window if it has 2766 square inches of glass?
Section 4.6 – Completing the Square
Problem 3:
What is the solution of
x2 + 4x + 4 = 25?
Section 4.6 – Completing the Square
Problem 3:
What is the solution of
x2 – 14x + 49 = 25?
Section 4.6 – Completing the Square
If x2 + bx is not part of a perfect square trinomial, you can use the coefficient b to find a constant c
so that x2 + bx + c is a perfect square.
When you do this, you are completing the square.
Section 4.6 – Completing the Square
When you do this, you are completing the square.
Section 4.6 – Completing the Square
When you do this, you are completing the square.
Section 4.6 – Completing the Square
Problem 4:
What value completes the square for x2 – 10x?
Justify your answer.
Section 4.6 – Completing the Square
Problem 4:
What value completes the square for x2 + 6x?
Justify your answer.
Section 4.6 – Completing the Square
Section 4.6 – Completing the Square
Problem 5:
What is the solution of 3x2 – 12x + 6 = 0?
Section 4.6 – Completing the Square
Problem 5:
What is the solution of 2x2 – x + 3 = x + 9?
Section 4.6 – Completing the Square
You can complete a square to change a quadratic function to vertex form.
Problem 6:
What is y = x2 + 4x – 6 in vertex form?
Name the vertex and y-intercept.
Section 4.6 – Completing the Square
Problem 6:
What is y = x2 + 3x – 6 in vertex form?
Name the vertex and y-intercept.
Section 4.6 – Completing the Square
Problem 6:
What is y = 2x2 – 6x – 1 in vertex form?
Name the vertex and y-intercept.
Section 4.6 – Completing the Square
Problem 6:
What is y = -x2 + 4x – 1 in vertex form?
Name the vertex and y-intercept.
Section 4.6 – Completing the Square
EXTRA PROBLEMS:
Solve the quadratic by completing the square:
x2 – x = 5
Section 4.6 – Completing the Square
EXTRA PROBLEMS:
Solve the quadratic by completing the square:
2x2 – ½x = 1/8
Section 4.6 – Completing the Square
EXTRA PROBLEMS:
Solve the quadratic by completing the square:
3x2 +x = 2/3
Section 4.6 – Completing the Square
EXTRA PROBLEMS:
Solve the quadratic by completing the square:
-.25x2 – 0.6x + 0.3 = 0
Section 4.6 – Completing the Square
EXTRA PROBLEMS:
Solve for x in terms of a:
2x2 – ax = 6a2
Section 4.6 – Completing the Square
EXTRA PROBLEMS:
Solve for x in terms of a:
6a2x2 – 11ax = 10
Section 4.6 – Completing the Square
EXTRA PROBLEMS:
Solve for x in terms of a:
4a2x2 + 8ax + 3= 0
Section 4.6 – Completing the Square
EXTRA PROBLEMS:
Solve for x in terms of a:
4a2x2 + 8ax + 3= 0
Section 4.6 – Completing the Square
Section 4.6 – Completing the Square