Algebra II : Functions and Graphs
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Example Questions
Example Question #52 : Polynomial Functions
Try without a calculator.
The graph of a function with the given equation forms a parabola that is characterized by which of the following?
None of these
Concave to the left
Concave to the right
Concave downward
Concave upward
Concave to the left
The graph of an equation of the form
is a horizontal parabola. Whether it is concave to the left or to the right depends on the sign of 
Example Question #602 : Functions And Graphs
How many 
Five
Zero
Ten
Two
One
One
The graph of a quadratic function 
The number of 
The discriminant is equal to zero, so the quadratic equation has one real zero, and the graph of 
Example Question #603 : Functions And Graphs
The vertex of the graph of the function
appears in __________.
None of these
Quadrant I
Quadrant IV
Quadrant II
Quadrant III
Quadrant I
The graph of the quadratic function 
Set 
Evaluate 
The vertex has a positive 
Example Question #51 : Polynomial Functions
The vertex of the graph of the function
appears in __________.
None of these
Quadrant IV
Quadrant III
Quadrant II
Quadrant I
Quadrant III
The graph of the quadratic function
Set 
Evaluate 
The vertex has a negative
Example Question #1 : Transformations Of Polynomial Functions
What transformations have been enacted upon 
vertical stretch by a factor of 4
horizontal stretch by a factor of 2
horizontal translation 6 units right
vertical stretch by a factor of 4
horizontal compression by a factor of 2
horizontal translation 6 units right
vertical stretch by a factor of 4
horizontal stretch by a factor of 2
horizontal translation 3 units right
vertical stretch by a factor of 4
horizontal compression by a factor of 2
horizontal translation 3 units right
vertical stretch by a factor of 4
horizontal compression by a factor of 2
horizontal translation 3 units right
First, we need to get this function into a more standard form.
Now we can see that while the function is being horizontally compressed by a factor of 2, it's being translated 3 units to the right, not 6. (It's also being vertically stretched by a factor of 4, of course.)
Example Question #1 : Transformations Of Polynomial Functions
Define 
Find 
By definition, 
Example Question #2 : Transformations Of Polynomial Functions
Define 
Find 
By definition, 
Example Question #3 : Transformations Of Polynomial Functions
Write the transformation of the given function moved five units to the left:
To transform the function horizontally, we must make an addition or subtraction to the input, x. Because we are asked to move the function to the left, we must add the number of units we are moving. This is the opposite of what one would expect, but if we are inputting values that are to the left of the original, they are less than what would have originally been. So, to counterbalance this, we add the units of the transformation.
For our function being transformed five units to the left, we get
Example Question #601 : Functions And Graphs
Write the transformation of the given function flipped, and moved one unit to the left:
To transform a function horizontally, we must add or subtract the units we transform to x directly. To move left, we add units to x, which is opposite what one thinks should happen, but keep in mind that to move left is to be more negative. To flip a function, the entire function changes in sign.
After making both of these changes, we get
Example Question #6 : Transformations Of Polynomial Functions
Transform the function by moving it two units up, and five units to the left:
To transform a function we use the following formula,
where h represents the horizontal shift and v represents the vertical shift.
In this particular case we want to shift to the left five units,
and vertically up two units,
Therefore, the transformed function becomes,
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