All Algebra II Resources
Example Questions
Example Question #52 : Transformations Of Linear Functions
Shift the equation left three units and up one unit.
Rewrite this equation in slope-intercept form, .
Shifting this equation up one unit will add one to the y-intercept.
The equation becomes:
To shift this equation left three units, we will need to replace the x-variable with the quantity .
Use distribution to simplify the equation.
The answer is:
Example Question #53 : Transformations Of Linear Functions
The line is shifted right 5 units. What must be the new equation?
If the line is shifted right 5 units, we will need to replace the x-variable of the equation with the quantity .
Simplify by distribution.
The answer is:
Example Question #54 : Transformations Of Linear Functions
Shift the equation up two units. What is the new equation?
Before we apply any transformations, we will need to put the equation in slope-intercept form, .
Subtract from both sides.
Divide by nine on both sides.
Shifting the equation up two units will add 2, or to the y-intercept.
The answer is:
Example Question #55 : Transformations Of Linear Functions
Shift the line to the left 8 units. What is the new equation?
To shift the line left 8 units, we will need to replace the x-value with .
Distribute the negative four through the binomial.
Combine like-terms.
The answer is:
Example Question #56 : Transformations Of Linear Functions
Shift the equation left eight units. What must be the new equation?
To shift the equation left eight units, replace the x-variable with the quantity of .
Simplify this equation.
Combine like-terms.
The answer is:
Example Question #57 : Transformations Of Linear Functions
If the equation is shifted left 9 units, what is the equation after the translation?
Rewrite the given line in standard form to slope-intercept format:
Subtract on both sides.
Replace the x-value with the quantity of since we are shifting the equation left 9 units.
Distribute the negative sign through both terms of the binomial.
The answer is:
Example Question #58 : Transformations Of Linear Functions
Translate the equation down six units. What is the new equation?
Use distribution to simplify the equation.
The equation in slope-intercept form is:
Shift the equation down six units means subtract the y-intercept by six.
The answer is:
Example Question #59 : Transformations Of Linear Functions
For the function we will define a linear transformation such that . Find the slope and y-intercept of the inverse function of .
Use the given function to find the linear transformation defined by .
First understand that in order to write we have to take our function and evaluate it for and then add to the result.
Adding ,
Now that we have , compute the inverse . Conventionally we replace the notation with the notation and solve for
Therefore,
At this point it's conventional to interchange and to write the inverse since we want to express it as a function of
Therefore the slope is and the y-intercept is
Example Question #59 : Transformations Of Linear Functions
Transform the equation into slope-intercept form.
In order to take an action from standard form to slope-intercept form you want to make it of the form:
where is the y-intercept (constant/number without a variable attached to it)
is the slope and coefficient of the term
and the equation is set equal to making it easier to plot graphically.
Given:
I. Isolate on one side of the equation. This is done by shifting either over to the other side of equation or the term and the constant to the other side of the equation. It is generally preferable to shift it to make so the term is positive by itself to simply operations and sign mixups. So in this case both and would be subtracted from both sides of the equation leaving:
II. Now that is isolated by itself you want to simplify the equation so there is no coefficient other than attached to , so in this case it'd mean dividing both sides by leaving:
III. Simplify the expression. If you are given fractions that are divisible by each other they can be simplified.
In the case is simplified to and is simplified to leaving the final answer of:
Example Question #1 : Quadratic Functions
Write a quadratic equation having as the vertex (vertex form of a quadratic equation).
The vertex form of a quadratic equation is given by
Where the vertex is located at
giving us .