Download quadratic formulasanswers deleted

Please Focus
as we review to prepare ourselves
for quadratic equations!
Solving Equations
► “It’s
impossible to solve a single equation
with two variables and get a single
solution.”
► “For example, for the equation”
3x + 2y = 100
if x=0 y=50, if x=5 y=85, if x=10 y=35…….
► We solved equations like this by making a
chart and choosing any number for x and
solving for y.
Solving Equations (continued)
► We
also solved these by putting them in
slope-intercept form and graphing them.
Standard form- Ax + By = C
3x + 2y = 100
Slope intercept formy = mx +b m=slope, b=y intercept
y = -3/2 x + 50
Classifying equations with 2
variables.
On your paper make a t-chart with 2
columns: Standard form/ Slope intercept
Put the following equations in the correct
column.
1. 3x + 2y = 17
2. 7/2x – 4y = -20
3. y = 1/2 x + 6 4. x + y = 4
5. y = -2x – 8
6. y=5
►
Standard Form
3x + 2y = 17
7/2x – 4y = -20
x+y=4
y intercept form
y = 1/2 x + 6
y = -2x – 8
y=5
Now for each problem write
A=
B=
C=
m=
b=
Linear Systems


For some problems, two equations
were needed. If you have two
equations with two variables each,
only one value of x and one value of
y will make both equations true.
For example- in Standard form3x - 2y = 5
3x + 2y = 13
x=3 y=2
Linear Systems (continued)
What three ways did we use to solve
linear systems?

Substitution

Elimination

Graphing
Linear Systems (continued)

What three ways did we use to solve
linear systems?

Substitution – put y by itself in one equation
and substitute it into the other and solve for x

Elimination- addition, subtraction,
multiplication
Graphing- put both equations in slope intercept
form. Where the two lines interceptThat’s the solution!!!!!

Quadratic Equations
“A quadratic equation is an equation with
a variable to the second power but no
variable higher than the second power.”
 “A quadratic equation has the form
ax2 + bx + c = 0
where a is not equal to zero”

Quadratic Equations

“Examples –





A. X2 + 3x + 5 = 0
B. 3x2 - 4x + 3 = 0
C. -5x2 - 2x = 7
D. X2 + 3x = 0
E. X2 – 36 =0
For each of these examples please writea=
b= c=
Quadratic Equations

For the following equations write “yes” if
it is a quadratic equation and “no” if not.
A.
 B.
 C.
 D.
 E.

x2 + 4x -9 = 0
x2 – 4x - 6
X3 – 4x2 + 6 =0
2x - 6 = 0
-3x2 -45 =0
Quadratic Equations

Q E can be solved in three main ways–
–
–
Graphing
Factoring
Quadratic Formula
Quadratic Equations

The quadratic formula is