# A rather straight forward function question.

• Dangshnizzle
In summary, the problem is to find the value of 'a' that makes the function f(x) = ax2-4 pass through three vertices of a square centered at the origin with its vertices on the x- and y- axes. Multiple solutions may exist, but only one is needed. Showing work and explaining the solution would be helpful. The value of 'a' can be found to be 0.25 by plugging in x = 0 and getting f(0) = -4, which corresponds to one of the vertices. It is also noted that the vertices of the square are located at (4,0), (-4,0), (0,4), and (0,-4).
Dangshnizzle
The problem statement:
A square centered at the origin has its vertices on the x- & y- axes.
The graph of the function f(x)=ax2-4 , a>0
Passes through three of the square's vertices.
You must find what 'a' makes this statement true.
Other things to know:
Well I think there are multiple solutions to the problem. But I only need one. It would really help if you could show work and explain how you got your answer.
Thanks in advance to anyone who assists.

Solved:
f(x)=(0.25)X2-4

'a'=0.25

Last edited:
If you plug in x = 0, you get f(0) = -4. That gives you one of the vertices, right?

jbunniii said:
If you plug in x = 0, you get f(0) = -4. That gives you one of the vertices, right?
Yeah so you are saying that because it is a square, it has to have vertices at
(4,0),(-4,0),(0,4), and (0,-4)? Hahah genius. So now it's much simpler to find the formula for what 'a' must be.

Dangshnizzle said:
Yeah so you are saying that because it is a square, it has to have vertices at
(4,0),(-4,0),(0,4), and (0,-4)? Hahah genius. So now it's much simpler to find the formula for what 'a' must be.
Yes, that's right.

jbunniii said:
Yes, that's right.
Solved:
f(x)=(0.25)X2-4

'a'=0.25

## 1. What is a function?

A function is a block of code that performs a specific task and can be called multiple times in a program. It takes in input, performs some operations on it, and produces an output.

## 2. What is the purpose of a function?

The purpose of a function is to break down a complex task into smaller, more manageable tasks. This makes the code more organized, easier to read, and allows for code reuse.

## 3. How do you define a function?

A function is defined using the keyword "function", followed by the function name, a set of parentheses, and curly brackets that contain the code to be executed.

## 4. What is a return statement?

A return statement is used to end the execution of a function and return a value back to the caller. It can also be used to specify the output of the function.

## 5. What is a parameter?

A parameter is a variable that is used to pass data into a function. It is defined in the function declaration and acts as a placeholder for the actual value that will be passed in when the function is called.

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