Upload
austin-ball
View
218
Download
1
Tags:
Embed Size (px)
Citation preview
What do the following slides have in common?
You’re thinking bridges, right?
Guess again!
Architecture?
Still no!
Motion
Throwing a ball Archery Catapult
Satellite Dishes
Any idea?
Parabolas
Common architectural design. Common engineering design. Shows motion of a projectile. They just look cool.
Chapter 6
Quadratic Equations
And
Functions
Ax2 is the “quadratic term”. Bx is the “linear term”. C is the constant term.
cbxaxy 2
Classify the following as quadratic, linear, or neither. Y=5x2-6
Y=3x-8
Y=4x3 + 2x2 -5x + 1
Y=-3x2
Quadratic
Linear
Neither
Quadratic
What if the function isn’t in quadratic form? We will simplify it in order to put it into that
form!
7)5(4)( 2 xxf
7)2510(4 xx
7100404 2 xx
107404 2 xx
Axis of Symmetry x = #
Vertex (h,k)
Axis of Symmetry x = #
Vertex (h,k)
Once you find the x-coordinate, plug that value into the function to find the matching y-coordinate.
Find the vertex.
a
bx
2
y
x
X-intercepts (a.k.a. roots or zeros)
Interesting things tend to happen at these locations. Vertex
X-intercepts
Axis of Symmetry
Highest or lowest point.
When an object hits the ground.
When an object changes direction.
a= 2 and b = -8
x = 8/4, so x = 2.
y = 2(4)-8(2)+4, so y = -4.
The vertex is (2, -4).
482 2 xxy
Find the x-intercepts.
Solve the quadratic equation using one of the following methods:
Graphing Factoring Completing the Square Quadratic Formula
Ok, it will take a little time to cover all of those different methods. Focus on graphing. Let’s use calculators! Yes, the graphing kind.
Graph. Hit 2nd, Calc. Choose the “Zero” option. Follow the commands.
482 2 xxy
Your x-intercepts are:
(.59,0) and (3.41,0)
What are the pro’s and con’s of this method? The calculator does all
of the work. The answer may be an
approximation. This may be more
difficult if your calculator cannot “see” the intercepts.
What if the intercepts are not real?
More practice?
Page 339
20, 22, 26, 30, 32, 35, 36, 40 , 44