All Algebra II Resources
Example Questions
Example Question #181 : Functions And Graphs
Which of the following represents a standard parabola shifted up by 2 units?
Begin with the standard equation for a parabola: .
Vertical shifts to this standard equation are represented by additions (upward shifts) or subtractions (downward shifts) added to the end of the equation. To shift upward 2 units, add 2.
Example Question #4 : Transformations
Which of the following transformation flips a parabola vertically, doubles its width, and shifts it up by 3?
Begin with the standard equation for a parabola: .
Inverting, or flipping, a parabola refers to the sign in front of the coefficient of the . If the coefficient is negative, then the parabola opens downward.
The width of the parabola is determined by the magnitude of the coefficient in front of . To make a parabola wider, use a fractional coefficient. Doubling the width indicates a coefficient of one-half.
Vertical shifts are represented by additions (upward shifts) or subtractions (downward shifts) added to the end of the equation. To shift upward 3 units, add 3.
Example Question #5 : Transformations
Which of the following shifts a parabola six units to the right and five downward?
Begin with the standard equation for a parabola: .
Vertical shifts to this standard equation are represented by additions (upward shifts) or subtractions (downward shifts) added to the end of the equation. To shift downward 5 units, subtract 5.
Horizontal shifts are represented by additions (leftward shifts) or subtractions (rightward shifts) within the parenthesis of the term. To shift 6 units to the right, subtract 6 within the parenthesis.
Example Question #6 : Transformations
Which of the following transformations represents a parabola that has been flipped vertically, shifted to the right 12, and shifted downward 4?
Begin with the standard equation for a parabola: .
Horizontal shifts are represented by additions (leftward shifts) or subtractions (rightward shifts) within the parenthesis of the term. To shift 12 units to the right, subtract 12 within the parenthesis.
Inverting, or flipping, a parabola refers to the sign in front of the coefficient of the . If the coefficient is negative, then the parabola opens downward.
Vertical shifts are represented by additions (upward shifts) or subtractions (downward shifts) added to the end of the equation. To shift downward 4 units, subtract 4.
Example Question #7 : Transformations
Which of the following transformations represents a parabola that has been shifted 4 units to the left, 5 units down, and quadrupled in width?
Begin with the standard equation for a parabola: .
Horizontal shifts are represented by additions (leftward shifts) or subtractions (rightward shifts) within the parenthesis of the term. To shift 4 units to the left, add 4 within the parenthesis.
The width of the parabola is determined by the magnitude of the coefficient in front of . To make a parabola wider, use a fractional coefficient. Doubling the width indicates a coefficient of one-fourth.
Vertical shifts are represented by additions (upward shifts) or subtractions (downward shifts) added to the end of the equation. To shift downward 5 units, subtract 5.
Example Question #1 : Transformations
If the function is shifted left 2 units, and up 3 units, what is the new equation?
Shifting left 2 units will change the y-intercept from to .
The new equation after shifting left 2 units is:
Shifting up 3 units will add 3 to the y-intercept of the new equation.
The answer is:
Example Question #1 : Transformations
If , what is ?
It is the same as .
It is the parabola reflected across the x-axis.
It is the parabola shifted to the right by 1.
It is the function.
It is the parabola reflected across the y-axis.
It is the parabola reflected across the x-axis.
It helps to evaluate the expression algebraically.
. Any time you multiply a function by a -1, you reflect it over the x axis. It helps to graph for verification.
This is the graph of
and this is the graph of
Example Question #10 : Transformations
If , what is ?
It is the graph shifted 1 to the right.
It is the graph reflected across the y-axis.
It is the graph reflected across the x-axis.
It is the graph rotated about the origin.
It is the graph.
It is the graph reflected across the y-axis.
Algebraically, .
This is a reflection across the y axis.
This is the graph of
And this is the graph of
Example Question #11 : Transformations
Transformations
Where will the point be located after the following transformations?
- Reflection about the x-axis
- Translation up 3
- Translation right 4
Where will the point be located after the following transformations?
- Reflection about the x-axis results in multiplying the y value by negative one thus .
- Translation up 3, means to add three to the y values which results in .
- Translation right 4, means to add four to the x value which will result in .
Example Question #12 : Transformations
Find the equation of the linear function obtained by shifting the following linear function along the x-axis 3 units to the left. State the y-intercept of .
y-intercept
y-intercept
y-intercept
y-intercept
y-intercept
y-intercept
The transformation for a left shift along the x-axis for requires we add to the argument of the function .
The y-intercept of the linear function is .