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Quadratic Functions

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by

Sam Baker

on 16 January 2014

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Transcript of Quadratic Functions

y=0
Quadratic Functions
Graphing a Quadratic Function
Discriminant
Word Problem
The height in feet of a bottle rocket is given by h(t)= 160t-16t where t is the time in seconds. How long will it take for the rocket to return to the ground? What is the height after 2 seconds?
Finding Roots
By: Sam Baker and Allan Andrews
Vocabulary
Axis of Symmetry
The line that goes through the middle of a parabola and through the vertex to create two equal sections.
Discriminant
b
2
- 4ac
When the letters from
ax
2
+bx+ c = 0
are pulled out into
the discriminant, the out come determines how many solutions the equation has.
Maximum/ Minimum Point
Quadratic Formula
Standard Form
Vertex
Vertex Form
Zeros/ Roots/ Intercepts
2
Using Factoring
Using the Quadratic Formula
Opens up or down
Axis of Symmetry
Vertex
Writing a Quadratic Equation
Given the roots
Standard form to vertex form
Vertex form to standard form
The highest point of the graph is called the maximum point. This is caused from the coefficient being greater then zero.
The lowest point of the graph is called the minimum point. This is caused from the coefficient being less then zero.
Formula to solve quadratic equations.
ax
2
+
The vertex is the highest or lowest point in a parabola including the y-coordinate and x- coordinate.
X=
____
-b
2a
The zeros are when y=0 the two x intercepts are the zeros.
These are also the roots to the quadratic equation.
At 10 seconds the rocket will hit the ground
After 2 seconds the height of the bottle rocket will be 256.
x
2
+ 3x+ 2=0
2
1
(x+2)(x+1)=0
x+2=0
x+1=0
The roots are -2 and -1
x
2
+ 3x+ 2=0
a=1
b=3
c=2
Plug in the numbers into the formula.
The roots are -2 and -1
x
2
+3x+2=0
Plug the numbers into the discriminant.
The discriminant equals 1. There for there is 2 real roots.
x=-2
x=-1
(x+2)(x+1)=0
Now foil
x
2
+3x+2
no real solutions
one real solutions
two real solutions
ax
2
2
is the quadratic term
is the linear term
is the constant term
bx
bx
+
c
c
=0
b
2
-4
a
c
a=1
b=3
c=2
1(x+1.5)
2
+.25
y=x
2
+3x+2
x
2
+3x +2
1(x-1.5)
2
+.25
To determine if a parabola opens up or down you look at your quadratic term.
y=x
2
y=-x

2
If the parabola opens up the quadratic term is positive.

If the parabola opens down the quadratic term is negative
f(x)= x
2
+2x+1
(x+1)
(x+1)
x=-1

f(x)= -1
2
-2+1
x=-1
To find the vertex just plug the axis of symmetry back into your original problem
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