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Quadratics and Roots
By Petrain King
IMaST Lead Coach
LAUSD
Modified from a PowerPoint, of the same
Title, by Mark P
http://subjectsearch.wikispaces.com/Math
Chapter 13-4 of Prentice Hall
• Memorize this equations
2
-b±√b -4ac
2a
•How many solutions?
–The discriminant knows
What are quadratic
equations?
• Any equation of the form:
y=ax2+bx + c
• The highest power of the variable is:
2
Roots
Page 591: Quadratic equations solve for two realnumber solutions.Some have 1 or no realnumber solutions.
Roots= solution.
Roots
Where are they in this example?
Y=height Height
Root
Root
X= Time
Objective: Use discriminant to
find the number of solutions for
a quadratic equation.
• So far we have had two real-number
solutions
• Some only have 1 or non.
• But how can I tell if it’s one, two, or
non?
Discriminant= b2-4ac
Discriminant=
2
b -4ac
0=x2 + 2x - 3
2
Discriminant = 2 -(4) (1) (-3)
Discriminant=16
If the discriminant is
positive=== two real numbers.
Discriminant=
2
b -4ac
0=x2 + 4x + 4
2
Discriminant = 4 -(4) (1) (4)
Discriminant=0
If the discriminant is
Zero === one real number
solutions.
Discriminant=
2
b -4ac
0 = x2 + x + 5
2
Discriminant = 1 -(4) (1) (5)
Discriminant= -19
If the discriminant is
Negative === no real-number
solutions.
If the discriminant is
positive=== two real
numbers
If the discriminant is
Zero=== one real-numbers
If the discriminant is
Negative = No real-numbers
Not on the
x axis at all
Homework
• Page 593
– Problems 19-27
Using Quadratic Equations.
One example
The path of a soccer ball kicked into
the air can be described by this
quadratic:
h = -16x2 + 10x + 3
t = time
H = height= y
Time is along the X axis
Using Quadratic Equations.
One example
The path of a soccer ball kicked into the
air can be described by this quadratic:
h = -16t2 + 10t + 3
t = time
H = height= y
Time is along the X axis
X = time= t
Roots
Using Quadratic Equations:
One example
• The path of a soccer ball kicked into the air
can be described by this quadratic:
h = -16t2 + 10t + 3
(h=height, t=time)
Time is along the X axis.
• If we solve for t, with the quadratic
equation, we can find where the ball started
and ended.
y = height
Roots
X = time= t
h = -16t2 + 10t + 3
Solving Quadratic Equations.
• To solve the quadratic equation for t we
must use the Quadratic Formula. Have
you memorized it yet?
t = -b ±
√b2 - 4ac
2a
h = -16t2 + 10t + 3
Solve for t
t
t
t
t
t
t
T= -0.22
T= 0.85
Roots
-0.22
0.85
X
•
•
•
•
•
•
•
•
•
•
•
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
Y
-447.00
-293.00
-171.00
-81.00
-23.00
3.00
-3.00
-41.00
-111.00
-213.00
-347.00