DO NOW

1. Use the discriminant to determine the number

and type of roots of:

a. 2x2 - 6x + 16 = 0 b. x2 – 7x + 8 = 0

2. Solve using the quadratic formula:

-3x2 – 8x + 5 = 0

3. Which method would you use to solve this and why?

8x2 - 32 = 0

4. Solve using the square root method (2x-1)2 = 6

WRITING QUADRATICS &

SYSTEMS OF LINEAR/QUAD

EQUATIONS

QUICK REVIEW…

GIVEN THE POINTS….FIND THE EQUATION!

� Sometimes we will be given data in a table or a

list of points and asked to write the equation

STEPS A=___ B=___ C= ___

� STAT - #1 Edit

� Enter X values in L1

� Enter Y values or f(x) in L2

� STAT CALC

� CALC - #5 QuadReg

� Go down to Calculate

� Put in the “a” “b” “c” values

to form a quadratic

EXAMPLE-PUT IN A TABLE!

a = ______ b = ______ c = ________

Equation:

(–2, 1), (–1, 0), (0, 1), (1, 4), (2, 9)

YOU TRY!

a = ______ b = ______ c = ________

Equation:

(–1, 10), (0, 3), (1, 0), (2, 1)

EXAMPLE

� The following data forms a parabola, what are the

roots? Find the equation.

x y

-4 8

-3 0

-2 -6

0 -12

4 0

5 8

HOW COULD YOU WRITE THE EQUATION FROM

LOOKING AT THE GRAPH?

� Find the zeros, write out the factors, and multiply out!

EXAMPLE:

What if the parabola opens down?

YOU TRY! FIND THE EQUATION!

�Last year we studied systems of

linear equations.

�We learned three different

methods to solve them.

�Elimination, Substitution and

Graphing

GRAPHING METHOD

�To solve is to find the intersections of the graph.

�Put each in slope intercept form and graph

�This is what we will use to solve a Quadratic/Linear System

CALCULATOR NOTES

1. Type equation 1 = y1, equation 2 = y2

2. Push 2nd�TRACE�5, move cursor to the left intersection push ENTER 3 times.

3. Push 2nd�TRACE�5, move cursor to the right intersection push ENTER 3 times.

EXAMPLE 1-ONE SOLUTION

−=+

−=+−

53

1042

yx

yx

EXAMPLE 2-NO SOLUTIONS

−=+

−=+

7102

105

yx

yx

EXAMPLE 3-INFINITE SOLUTIONS

−=+−

=−

264

132

yx

yx

LINEAR AND QUADRATIC SYSTEMS OF

EQUATIONS

� Today we will learn about systems of quadratic

AND linear equations.

� You can use graphing or substitution

GRAPHING METHOD� We do this the same way we do linear equations

� To solve is to find the intersections of the graph.

+−=

+=

14

3

2xxy

xy

GRAPHS & SOLUTIONS

How can we CHECK our answers?

EXAMPLE #2

EXAMPLE #3:

−=

+−=

6

332

xy

xxy

SUBSTITUTION METHOD

�If we know that y = y. Then you

can set both of the right hand

sides of the equations equal.

+−=

+=

14

3

2xxy

xy

Example 1:

x2 – 4x + 1 = x + 3

+−=

+=

14

3

2xxy

xy

+−=

+=

105

5

2xxy

xy

EXAMPLE 2:

x + 5 = x2 – 5x + 10

EXAMPLE #3 –YOU CHOOSE

METHOD!

+=

−+=

12

322

xy

xxy

EXAMPLE #4 – YOU CHOOSE

METHOD!

+=

++−=

6

652

xy

xxy

EXAMPLE #5 – YOU CHOOSE

METHOD!

4

602

y = x +

+ x - y = x

WORD PROBLEM

� The weekly profits of two different companies

selling similar items that opened for business at

the same time are modeled by the equations

shown below. The profit is represented by y and

the number of weeks the companies have been in

business is represented by x. According to the

projections, what week(s) did the companies have

the same profit? What was the profit of both

companies during the week(s) of equal profit?

�Company A: y = x2 – 70x + 3341

�Company X: y = 50x + 65

REASONING

The graph at the right shows a quadratic function and the linear function x = b.

How many solutions does this system have?

Will the number of solutions be the same for any value of b?Explain.

If the linear function were changed to y = b, would the number of solutions be the same for any value of b?

CHALLENGE PROBLEM FOR CANDY!

� Reasoning What are the solutions of the system

y = 2x2 – 11 and y = x2 + 2x – 8? Explain how you

solved the system.

HOMEWORK

� Begin working on the Practice Test for

Quadratics!