Question

1) Create a quadratic function, f(x), in vertex form. The a should be between 4 and –4, the h will be your birth month, and the k will be your birth day. Write your equation below.
I did this, I got y=2(x-4)^2+3

However, I need some help with the rest please. If you could help explain it to me so I can do it in the future, that would be great. Thank you(:

Answer 1

2) Create two additional quadratic functions, g(x) and h(x).
The function g(x) will open the same direction as f(x), have the same vertex, but will be narrower.
The function h(x) will open in the opposite direction as f(x), have the same vertex, but will be wider than f(x).
Write your functions below and explain in complete sentences why those functions will meet the requirements in the question.

Answer 2

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIyKHgtNCleMiszIiwiY29sb3IiOiIjMDAwMDAwIn0seyJ0eXBlIjoxMDAwLCJ3aW5kb3ciOlsiLTMyLjc2Nzk5OTk5OTk5OTk5IiwiMzIuNzY3OTk5OTk5OTk5OTkiLCItMjEuNDg0OTIzMDc2OTIzMDY3IiwiMTguODQ0OTIzMDc2OTIzMDY3Il19XQ-- <--- notice your function

change the "a" value to a BIGGER number, press Tab, see what happens
change the "a" value to a SMALLER number, press Tab, see what happens
change the "a" value to a NEGATIVE number, press Tab, see what happens

Answer 3

So for the function g(x), would g(x)=5(x-4)^2+3 work?

Answer 4

yeap, something bigger than the original, so bigger than 2
something smaller than the original, will make it wider
try say 1/2 in the graph for example

a negative value to it, will simply flip it upside-down

Answer 5

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIyKHgtNCleMiszIiwiY29sb3IiOiIjMDAwMDAwIn0seyJ0eXBlIjowLCJlcSI6IjUoeC00KV4yKzMiLCJjb2xvciI6IiMxQjE0RTAifSx7InR5cGUiOjAsImVxIjoiMS80KHgtNCleMiszIiwiY29sb3IiOiIjRUQxNzE3In0seyJ0eXBlIjowLCJlcSI6Ii0xLzQoeC00KV4yKzMiLCJjb2xvciI6IiNFMzBEQjEifSx7InR5cGUiOjEwMDAsIndpbmRvdyI6WyItMjkuNTQxNjEyMzA3NjkyMjk0IiwiMzUuOTk0Mzg3NjkyMzA3Njc2IiwiLTE0LjAyMzkwMTUzODQ2MTUzMiIsIjI2LjMwNTk0NDYxNTM4NDYwNCJdfV0-

Answer 6

5) Using complete sentences, explain how to find the average rate of change for f(x) from x = 4 to x = 7.

Answer 7

in short, it'd be the difference of f(7) and f(4)
divided by how many units in between, thus \(\bf \cfrac{f(7)-f(4)}{7-4}\)

Answer 8

Last Question. Explain the appropriate translations of your graphs, if you were born two months earlier and 5 days later. Use complete sentences.

Answer 9

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIyKHgtNCleMiszIiwiY29sb3IiOiIjMDAwMDAwIn0seyJ0eXBlIjowLCJlcSI6IjIoeC0oNC0yKSleMiszIiwiY29sb3IiOiIjRTYxOTE5In0seyJ0eXBlIjowLCJlcSI6IjIoeC00KV4yKygzKzUpIiwiY29sb3IiOiIjMUQxN0QxIn0seyJ0eXBlIjoxMDAwLCJ3aW5kb3ciOlsiLTMyLjc2Nzk5OTk5OTk5OTk5IiwiMzIuNzY3OTk5OTk5OTk5OTkiLCItMjEuNDg0OTIzMDc2OTIzMDY3IiwiMTguODQ0OTIzMDc2OTIzMDY3Il19XQ--

Answer 10

So the graph would become smaller and narrower?

Answer 11

\(\large{ \begin{array}{llll}
&&\textit{vertical shift, + up, - down}\\
&&\downarrow \\
y = A ( x + &C ) + &D\\
&\uparrow \\

\end{array}\\\textit{horizontal shift, + to the left, - to the right}}\)

Answer 12

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIyKHgtNCleMiszIiwiY29sb3IiOiIjMDAwMDAwIn0seyJ0eXBlIjowLCJlcSI6IjIoeC0oNC0yKSleMiszIiwiY29sb3IiOiIjRTYxOTE5In0seyJ0eXBlIjowLCJlcSI6IjIoeC00KV4yKygzKzUpIiwiY29sb3IiOiIjMUQxN0QxIn0seyJ0eXBlIjoxMDAwLCJ3aW5kb3ciOlsiLTMyLjc2Nzk5OTk5OTk5OTk5IiwiMzIuNzY3OTk5OTk5OTk5OTkiLCItMjEuNDg0OTIzMDc2OTIzMDY3IiwiMTguODQ0OTIzMDc2OTIzMDY3Il19XQ-- <--- notice the units the graph went to the left
and to upwards

Answer 13

Alright. Thank you!

Answer 14

yw