Algebra II : Transformations of Parabolic Functions
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Example Questions
Example Question #11 : Transformations Of Parabolic Functions
Write the equation for 
Right now, the vertex for this point is 
This gives us an equation of 
We could also get this by adding 5 inside the parentheses for the left 5 shift, and adding 4 on the outside for the up 4 shift.
Example Question #31 : Parabolic Functions
Give the equation of the parabola 
Flipping this equation over the x-axis means that the sign of y changes.
The easiest way to accomplish this is just to multiply everything by -1.
Example Question #13 : Transformations Of Parabolic Functions
Which would be the equation of 
To flip this over the 
This entails changing 
Perhaps a simpler way to think about this is that the vertex for this parabola is at 
If we flip the equation over the y-axis, it will place the vertex at 
Example Question #14 : Transformations Of Parabolic Functions
Write the equation for the parabola 
To solve this problem, we could complete the square and shift the equation that way, but the vertex ends up being 
To simplify, first expand
Now we can plug that in and continue simplifying:
Now we want to flip this over the x-axis, meaning that the y coordinates change sign.
This means we have to multiply everything by -1, or simply change the sign of every term on the right side:
Example Question #41 : Parabolic Functions
Describe the translation in
from the parent function
Up three units, left one unit
Up three units, right one unit
Down three units, right one unit
Down three units, left one unit
Down three units, right one unit
Below is the standard equation for parabolas;
Therefore,
thus,
the translation from the parent function is down three units, right one unit.
Example Question #14 : Transformations Of Parabolic Functions
Given the parabola 
Shifting up and down will result in a change in the y-intercept.
Add four to the equation.
Shifting the parabola to the left two units will change the inner term 
Replace the 
The new equation is:
Example Question #15 : Transformations Of Parabolic Functions
Shift 
Vertical shifts will change the value of the y-intercept. Since this function is to be shifted up two units, add two to the right side of the equation.
This graph shifted two units to the left indicates that its zeros will also shift to the left two units, which means that the 
Rewrite the equation and expand the binomials.
The new equation is:
Example Question #16 : Transformations Of Parabolic Functions
Shift the parabola 
Shifting this graph three units to the right means that the x-variable will need to be replaced with 
Use the FOIL method to simplify the binomial.
Simplify the right side.
The equation becomes:
The answer is:
Example Question #42 : Parabolic Functions
3 spaces right
3 spaces up
3 spaces down
3 spaces left
3 spaces right
Example Question #43 : Parabolic Functions
Which of the below quadratic functions will be the widest?
To determine how "wide" or "skinny" a parabola is, we look at the leading coefficient.
The smaller the fraction, the wider a parabola will be.
The larger the whole number, the skinnier the parabola will be.
This will give us the widest parabola.
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