Section 5-4 Completing The Square & Quadratic Formula
EASY
x 2 10 x 6 0
x 2 10 x 6 0
+6
+6
x 2 10 x
of
10
5
Move constant to the other side
6
x 2 10 x 25 6 25
Square
It
25
x 2 10 x 25 31
Easily Factors
x 5x 5 31
x 52 31
x 52 31
Can be re-written
Take the
(
)
Name:
Solve the following QUADRATIC EQUATIONS using the SQUARE ROOT METHOD:
2
1. w 16 0
2
2. 2 y 48 0
2
3. 4m 196
5. 3x 1 2 14
1
4 a 1 5 31
6. 2
2
4. b 2 36
2
2
Solve the following QUADRATIC EQUATIONS by FACTORING & ZERO PRODUCT PROPERTY:
2
1. w 2w 24
Name:
Not all may be possible.
1. Find two numbers that sum to 8 and have a product of 12 _
2. Find two numbers that sum to 5 and have a product of 6 _
3. Find two numbers that sum to 5 and have a product of -14 _
4. Find two numbers that sum to -6 and ha
A Parable about Parabolas
Name:
What is a parabola?
It is geometrically defined by a set of points or locus of points that are
equidistant from a point (the focus) and a line (the directrix).
To see this idea visually try
drawing a straight line at the
bo
A Soliloquy about Circles
Name:
What is a circle?
It is geometrically defined
by a set of points or locus of points that are equidistant
from a point (the center). Consider the circle at the
right. What is the length of every segment drawn from
center O t
Transformations in the Coordinate Plane
Name:
Symmetry
Symmetries
A shape has a vertical line of
symmetry if you can fold it in half
vertically and have the halves match up.
On a scrap sheet of paper try folding the
letter M in half.
A shape has a horizon
Intersection of Curves
Name:
1. Create a picture of a circle
and line that dont
intersect.
3. Create a picture of a
circle and line that
intersect once.
5. Create a picture of a
circle and a parabola
that intersect twice.
7. Create a picture of a
circle a
Transformations in the Coordinate Plane
Identifying Types of Transformations
Name:
Transformation Types:
Translation
Translation
Rotation
Dilation
Dilation
Image
Pre-Image
Translations
1. Describe the transformation in rectangular units from the Pre-Image
Transformations in the Coordinate Plane
Name:
Coordinate Transformations
Transformation Types:
Translation
Translation
Rotation
Image
Pre-Image
Translations
1. Plot the points and create the pre-image triangle
with vertices M( 2, 3), N(3, 5), and P (5,2).