The portion results in the graph being shifted 3 units to the left, while the results in the graph being shifted six units down. Vertical shifts are the same sign as the number outside the parentheses, while horizontal shifts are the OPPOSITE direction as the sign inside the parentheses, associated with .

The function shifts a function f(x) units to the left. Conversely, shifts a function f(x) units to the right. In this question, we are translating the graph two units to the left.

To translate along the y-axis, we use the function or .

Below is the standard equation for parabolas;

Therefore,

and

thus,

the translation from the parent function is down three units, right one unit.

To shift up 6 units, just add 6:

To shift to the right 3, subtract 3 from x:

First expand :

now this gives us:

distribute the 2 and the 4:

combine like terms:

Simplify the following equation by using the FOIL method with the binomial.

Simplify all terms in the parentheses.

Replace the term and simplify.

The equation in standard form is:

Since this parabola is shifted up one unit, add one to the y-intercept.

The answer is:

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 to , which will be .

Replace the quantity with .

The new equation is:

When transforming paraboloas, to translate up, add to the equation (or add to the Y).

To translate to the left, add to the X.

Don't forget that if you add to the X, then since X is squared, the addition to X must also be squared.

with the shift up 5 becomes: .

Now adding the shift to the left we get:

.

Shifting this graph three units to the right means that the x-variable will need to be replaced with . Rewrite the equation.

Use the FOIL method to simplify the binomial.

Simplify the right side.

The equation becomes:

The answer is:

The parent function of a parabola is where are the vertex.

The original graph of a parabolic (quadratic) function has a vertex at (0,0) and shifts left or right by h units and up or down by k units.

.

This function then shifts 1 unit left, and 4 units down, and the negative in front of the squared term denotes a rotation over the x-axis.

Correct Answer: