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. 2) Using complete sentences, explain how to convert your birthday function into standard form. 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. 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). Write your functions below and explain in complete sentences why those functions will meet the requirements in the question. 4) Graph your functions. Include your graph below. 5) Using complete sentences, explain how to find the average rate of change for f(x) from x = 4 to x = 7. 6) Explain the appropriate translations of your graphs, if you were born two months earlier and 5 days later. Use complete sentences.

Answer 1

My birthday is July 11. hence h is equal to 7 and k is equal to 11. The equation thus is (x-7)^2 = 2*4(y-11). The equation is expanded intp x^2 - 14x +49 = 8y - 88 or equivalent to  x^2 - 14 x + 137 - 8y = 0.  A wider latus rectum would mean a should be greater than 2, let's say 4. Hence the h(x) is equal to (x-7)^2 = 4*4(y-11) =16 y - 176. The expanded form is x^2 - 14 x + 49 = 16 y -176. This is equal to x^2 - 14 x + 225 - 16y = 0. A narrower graph means a less than 2, let's say 1. This is equal to (x-7)^2 = 1*4(y-11) or  g(x) = x^2 - 14 x + 93 - 4y = 0

Answer 2

1. y = (x - 8)² + 15 

2. The standard form is Ax² + By = C. Using a complete sentence the FOIL strategy on (x - 8)², I’d combine it with 15.

3A. y = 4(x - 8)² + 15 

3B. y = -0.1(x - 8)² + 15.

The value of “a” is similar to a slope. The bigger a is, the smaller the slope. Moreover, if a is negated then it will flip the graph.

5. The average change rate is equal to [f(7) - f(4)] / (7 - 4) and this means it’s simply the slope of the line among two points.

6. y = (x - 6)² + 20. This will move 2 units to the left and move up 5 units.

 

I am hoping that these answers have somewhat satisfied your query about these specific questions.