Game PlanSeptember 20th, 2010

- Do Now- Review Hmk

- Back to the Basics -Quadratic-Linear Systems

- U Try-Real World Example

- Focus QuestionsOpen House tmw

evening!

What does the little mermaid wear to math

class?

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 y = x2 + 4x – 2

II. Find Axis of Symmetry:a= b= c=

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: y = 5 – x2

II. Find Axis of Symmetry:a= b= c=

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) (3) (5, -4)(2) (-5, 6) (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!