SOLUTION: This is a word problem on a worksheet that I've been given. Katy likes to catch butterflies. The equation b = -2(x-4)^2 + 25 models this habit, where b is the number of butterfl

Question 169949: This is a word problem on a worksheet that I've been given.
Katy likes to catch butterflies. The equation b = -2(x-4)^2 + 25 models this habit, where b is the number of butterflies caught for the hour and x is the number of hours after she started catching. After how many hours will Katy catch the maximum amount?
I am stumped on this question. I don't even know where to start...
Please help, thanks.

I also have some questions on a form of quadratic function. I've only done quadratic functions that are in the form y= ax^2 + bx + c. So I'm not quite sure on these 3 multiple choice questions.

Here is the information:
One form of a quadratic function is f(x) = a(x-b)^2 + c.

Here are the questions:
1. If you wanted to shift the graph of the function up, what would you do?
A. increase a
B. decrease b
C. increase c
D. decrease a
2. If you wanted to shift the graph of the function left what would you do?
A. increase b
B. decrease b
C. increase c
D. decrease a
3. If you wanted to make the parabola wider, what would you do?
A. increase a
B. decrease b
C. increase c
D. decrease a
***Note:
For question 1 I chose letter c.
For question 2 I chose letter a.
For question 3 I chose letter d.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
This is a word problem on a worksheet that I've been given.
Katy likes to catch butterflies. The equation b = -2(x-4)^2 + 25 models this habit, where b is the number of butterflies caught for the hour and x is the number of hours after she started catching. After how many hours will Katy catch the maximum amount?
I am stumped on this question. I don't even know where to start...
Please help, thanks.
---
Your equation shows the vertex form of the quadratic. When x = 4, b=25
and that is the vertex of the prabola which opens downward from that point.
The maximum b-value occurs when x = 4
===============================================
I also have some questions on a form of quadratic function. I've only done quadratic functions that are in the form y= ax^2 + bx + c. So I'm not quite sure on these 3 multiple choice questions.
Here is the information:
One form of a quadratic function is f(x) = a(x-b)^2 + c.
Here are the questions:
1. If you wanted to shift the graph of the function up, what would you do?
A. increase a
B. decrease b
Ans: C. increase c
D. decrease a
--------------------------------
2. If you wanted to shift the graph of the function left what would you do?
A. increase b
Ans: B. decrease b
C. increase c
D. decrease a
--------------------------------
3. If you wanted to make the parabola wider, what would you do?
Ans: A. increase a
B. decrease b
C. increase c
D. decrease a
===========================
Cheers,
Stan H.
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