Download Linear Quadratic Systems PPT

Game Plan
September 20th, 2010
Open
House
tmw
evening!
What does the
little mermaid
wear to math
class?
- Do Now
- Review Hmk
- Back to the Basics
-Quadratic-Linear Systems
- U Try
-Real World Example
- Focus Questions
Focus Questions:
#1) What is a system on the coordinate
plane in math?
#2) What are the 3 possible solutions for
quadratic-linear systems?
Do Now:
Mixture of Various Ways to Write Linear
Equations
y = mx + b form (slope-intercept)
How to Write the Equation of a Line
Homework Time!
1.) Write an equation of a line whose slope is 2
and intersects the y-axis at -4.
2.) Write an equation of a line whose slope is -3
and passes through a point (2,5)
3.) What is the slope of a line perpendicular to
2y = -6x - 10?
4.) A line passes through a point (2,5) and has a
slope of -3. What is the equation of a line
perpendicular to this line through (2,5)?
5.) Given 4y - 2x = 10 and -6y - 6 = -3x.
Are these lines parallel, perpendicular or
neither?
6.) Write the equation of a line that passes
through the points (2,4) and (-3,-6)?
Einstein!
7.) The points (5, K) and ( 4, k) lie on the line
whose slope is 0, what is the value of K
Linear-Quadratic Systems
What is a system in Math?!
Graph a line y = mx + b
Graph a quadratic parabola ax2 + bx + c
Where such graphs intersect = solution
The 3 Possible Situations:
Back to the Basics:
Ways to Graph Them:
Solve graphically:
…means to graph both equations and see
where they intersect on the coordinate plane!
Remember a solution(s) are a point (x, y)
Example: Solve graphically:
y = x2 + 4x – 2
y = 2x + 1
I. Start w/ Quadratic
II. Find Axis of Symmetry:
a=
b=
c=
y = x2 + 4x – 2
III. Set up Table of Values:
y = x2 + 4x – 2
IV. Graph the parabola:
-Label w/ original
-Arrows
-Extend!!
Graph the line,
y = 2x + 1
m=
b=
Remember to:
-label w/ original
- arrows
-extend line
Find the point(s) of intersection: _______
House Keeping of Graphs
On Graphing Calculator
Example:
• Solve graphically:
y = 5 - x2
y=x+3
I. Rewrite in standard form:
II. Find Axis of Symmetry:
a=
b=
c=
y = 5 – x2
Set up Table of Values:
Graph the parabola:
y= 5 – x2
Graph the line, y = x + 3
m=
b=
Graphing Calculator Example:
Solve linear quadratic system:
y = x2 - 4x - 2
y+2=x
What must we do first to our linear equation?
Multiple Choice Example:
Which ordered pair is in the solution set of the
system of equations,
y= -x + 1 and y = x2 + 5x + 6?
(1) (-5, -1)
(2) (-5, 6)
(3) (5, -4)
(4) (5, 2)
Real World Example of a System:
Cora shoots a quarter from the top of a building
at the same time that Matt releases a Happy
Birthday balloon for Ally from the ground.
(What a coincidence?!) The equation
describing the height (y) above ground of the
quarter in feet is y = 64 – 2x2 where x is
seconds. The equation describing the
elevation of the balloon in feet is y= 6x + 8.
After how many seconds will the balloon and
quarter pass each other?
We are looking for when the y = 64 – 2x2 and
the y= 6x + 8 intersect!
Parabola:
Linear:
Graph Time!