5.5 Completing the Square (Part 2

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Algebra II Quarter 3: Handout #2
Name ________________________ Date _____________ Period _____
5.5 Completing the Square (Part 2 - Parabolas)

In this lesson we will apply the concept of “Completing the square” to
parabolas. This method will give information on the maximums and minimums.

What part of an equation tells us we will have a parabola when graphed?

What shape is a parabola?

What is the difference between a parabola that opens up and a parabola that
opens down? Draw and label a diagram!

What is the vertex of a parabola? What is the line of symmetry of a
parabola? Draw and label a diagram!
Memorize!!!
The general formula of a parabola is: y = (x – h)2 – k
The vertex is given by coordinates: (h, k)
The line of symmetry is given by the vertical equation: x = h
When you have x2 (positive,) the parabola opens upward and you have a minimum.
When you have –x2 (negative,) the parabola opens downward and you have a maximum.
Algebra II Quarter 3: Handout #2

Example 1: Write the quadratic function in vertex form.
y = x2 – 8x + 11
What is the vertex? ___________________________
What is the line of symmetry? _________________________
Will there be a max or min? Why? __________________________________
Draw and label simple picture:
Algebra II Quarter 3: Handout #2

Example 2: Write the quadratic function in vertex form.
y = x2 + 12x
What is the vertex? ___________________________
What is the line of symmetry? _________________________
Will there be a max or min? Why? __________________________________
Draw and label simple picture:
Algebra II Quarter 3: Handout #2

Example 3: Write the quadratic function in vertex form.
y = -x2 + 14x - 45
What is the vertex? ___________________________
What is the line of symmetry? _________________________
Will there be a max or min? Why? __________________________________
Draw and label simple picture:
Algebra II Quarter 3: Handout #2

Example 4: Write the quadratic function in vertex form.
y = 2x2 + 4x - 4
What is the vertex? ___________________________
What is the line of symmetry? _________________________
Will there be a max or min? Why? __________________________________
Draw and label simple picture:
Algebra II Quarter 3: Handout #2

Example 5: Write the quadratic function in vertex form.
y = x2 + 10x + 17
What is the vertex? ___________________________
What is the line of symmetry? _________________________
Will there be a max or min? Why? __________________________________
Draw and label simple picture:
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