Question

Help please! Ill give a medal out :))

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 birthday. Write your equation below.
h=12
k=25
:))

Answer 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.

General quadratic formula ...

y = a(x-h)² + k

choose a = 1 because it is easy to work with ...

y = (x - 8)² + 15



2) Using complete sentences, explain how to convert your birthday function into standard form.

Standard Form is ...

Ax² + By = C

So use FOIL on (x - 8)² and combine it with 15. Then put it in the Standard form above.


3) Create two additional quadratic functions, g(x) and h(x).
A. The function g(x) will open the same direction as f(x), have the same vertex, but will be narrower.

y = 4(x - 8)² + 15


B. The function h(x) will open in the opposite direction as f(x), have the same vertex, but will be wider than f(x).

y = -0.1(x - 8)² + 15

Write your functions below and explain in complete sentences why those functions will meet the requirements in the question.

The value of "a" is like a slope. The larger a, the narrower the slope. Also, if negate a, it will flip the graph.

4) Graph your functions. Include your graph below.

Use your TI calculator or graph by hand.


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

average rate of change = [f(7) - f(4)] / (7 - 4)

It is simply the "slope of the line" between the two points.


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


y = (x - 6)² + 20

Answer 2

Thank you !