Please enable JavaScript.
Coggle requires JavaScript to display documents.
Unit 5 - Applying Quadratic Models - Coggle Diagram
Unit 5 - Applying Quadratic Models
5.1 Stretching/Reflecting Quadratic Relations
A value
Affects y
This is from
y = a(x-h)^2 + k
y = ax^2 + bx + c
y = a(x - r)(x - s)
Different Values
a > 1
Parabola vertically stretches
"gets skinnier"
0 < a < 1
Parabola vertically compresses
"gets wider"
a < 0
Reflects in the x-axis
All of this is based on the equation y = x^2
STRETCH FACTOR IS ALWAYS POSITIVE
The a-value is not necessarily the stretch factor
The digit is the stretch factor
The sign does not play into the stretch factor
it is impossible to have a vertical stretch of -5 or any negative values
the negative value means that it is reflected in the x-axis - nothing else
5.2 - Exploring Translations of Quadratic Relations
All of this is based on y = x^2
y = a(x - h)^2 + k
k - affects the y-value of the vertex
in other words, it moves up/down
affects the x-value of vertex
in other words it goes left/right
x always lies ;-)
it is the opposite value of what you think it is
Change from y = x^2 to y = a(x - h)^2 + k
from y = x^2
(h, k)
The vertex
Since the vertex is (0, 0), the values of x and y are 0
h - affects x
a and k - affects y
5.3 Graphing Quadratics in Vertex Form
a value
difference in y-values
1, 3, 5
take these numbers and multiply by the a-value
1
1a
3
3a
Start at the vertex
Change x by -1 or 1
1 more item...
5
5a
y = x^2
(h, k)
k = Axis of symmetry
Vertex
k = Max/Min Value
Table Method
Make a table of values
Then sub in the values and you can get your points
Order of applying method
a value
translate the parabola
k value
h value
5.5 Solving Problems Using Quadratic Relations
How to convert between factored form, standard form or vertex form
Factored Form - f(x) = a(x - r)(x - s)
Expand
Standard Form - f(x) = ax^2 + bx + c
Complete the square and convert to vertex form
Vertex Form = f(x) = a(x - h)^2 + k
Expand
Factor
Find the axis - x = (r + s) / 2
Plug the axis back into the equation for the y-value
Sub in values of: a, h, and k
Fix, clean and simplify
Equations
f(x) = ax^2 + bx + c
a value - tells the stretch factor & if the parabola is upwards or downwards
c value - y-intercept
f(x) = a(x - h)^2 + k
a value - tells the stretch factor & if the parabola is upwards or downwards
h - the axis of symmetry
k - min/max value
f(x) = a(x - r)(x - s)
a value - tells the stretch factor & if the parabola is upwards or downwards
r and s values - the roots/zeros/solutions/x-intercepts
The average of the roots is the axis of symmetry
Vertex: ((r + s)/2, y)
Completing the Square
group the x-terms
take the middle number
divide it by 2
square it
Now that you have a perfect square, factor the equation
Simplify the equation
Now you have the equation in vertex form
