By definition, , so

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

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

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,

.

Expand the binomial.

Multiply negative by this quantity.

The polynomial in standard form is:  

Shifting this graph up one will change the y-intercept by adding one unit.

The answer is:  

Shifting this parabola up two units requires expanding the binomial.

Use the FOIL method to simplify this equation.

Shifting this graph up two units will add two to the y-intercept.

The answer is:  

We will need to determine the equation of the parabola in standard form, which is:

Use the FOIL method to expand the binomials.

Shifting this up two units will add two to the value of .

The answer is:  

In this problem, the  in the  equation becomes  --> .

This simplifies to , or

. 

To simplify a polynomial, we have to do two things: 1) combine like terms, and 2) rearrange the terms so that they're written in descending order of exponent.

First, we combine like terms, which requires us to identify the terms that can be added or subtracted from each other. Like terms always have the same variable (with the same exponent) attached to them. For example, you can add 1 "x-squared" to 2 "x-squareds" and get 3 "x-squareds", but 1 "x-squared" plus an "x" can't be combined because they're not like terms.

Let's identify some like terms below.

Here you can see that -4x and 9x are like terms. When we combine (add) -4x and 9x, we get 5x. So let's write 5x instead:

Let's do the same thing with the x-squared terms:

Now there are no like terms left. Our last step is to organize the terms so that x is written in descending power:

This is not a FOIL problem, as we are adding rather than multiplying the terms in parenteses.

Add like terms to solve.

Combining these terms into an expression gives us our answer.