Can someone me with this? i still have 2 more pages to do and i'm stressed out of my mind i honestly just wanna pass math so i can move on? ? so can someone me ?

1. First we are going to find the vertex of the quadratic function . To do it, we are going to use the vertex formula. For a quadratic function of the form , its vertex  is given by the formula ; .

We can infer from our problem that  and , sol lets replace the values in our formula:




Now, to find , we are going to evaluate the function at . In other words, we are going to replace  with -2 in the function:





So, our first point, the vertex of the parabola, is the point .

To find our second point, we are going to find the y-intercept of the parabola. To do it we are going to evaluate the function at zero; in other words, we are going to replace  with 0:



So, our second point, the y-intercept of the parabola, is the point (0,1)

We can conclude that using the vertex (-2,-7) and a second point we can graph  as shown in picture 1.

2. The vertex form of a quadratic function is given by the formula: 
where
is the vertex of the parabola.

We know from our previous point how to find the vertex of a parabola.  and , so lets find the vertex of the parabola .







Now we can use our formula to convert the quadratic function to vertex form:




We can conclude that the vertex form of the quadratic function is .

3. Remember that the x-intercepts of a quadratic function are the zeros of the function. To find the zeros of a quadratic function, we just need to set the function equal to zero (replace  with zero) and solve for .



To solve for , we need to factor our quadratic first. To do it, we are going to find two numbers that not only add up to be equal 4 but also multiply to be equal -60; those numbers are -6 and 10.

Now, to find the zeros, we just need to set each factor equal to zero and solve for .
and 
and 

We can conclude that the x-intercepts of the quadratic function are the points (0,6) and (0,-10).

4. To solve this, we are going to use function transformations and/or a graphic utility.
Function transformations.
- Translations:
We can move the graph of the function up or down by adding a constant  to the y-value. If , the graph moves up; if , the graph moves down.

- We can move the graph of the function left or right by adding a constant  to the x-value. If , the graph moves left; if , the graph moves right.

- Stretch and compression:
We can stretch or compress in the y-direction by multiplying the function by a constant . If , we compress the graph of the function in the y-direction; if , we stretch the graph of the function in the y-direction.

We can stretch or compress in the x-direction by multiplying  by a constant . If , we compress the graph of the function in the x-direction; if , we stretch the graph of the function in the x-direction.

a. The  value of  is 2; the  value of  is -3. Since  is added to the whole function (y-value), we have an up/down translation. To find the translation we are going to ask ourselves how much should we subtract to 2 to get -3?



Since , we can conclude that the correct answer is: It is translated down 5 units.

b. Using a graphing utility to plot both functions (picture 2), we realize that  is 1 unit to the left of 

We can conclude that the correct answer is: It is translated left 1 unit.

c. Here we have that  is  multiplied by the constant term 2. Remember that We can stretch or compress in the y-direction (vertically) by multiplying the function by a constant .

Since , we can conclude that the correct answer is: It is stretched vertically by a factor of 2.