# Finding transformations and base function of quadratic equation.

• calcdummy
It might be a good idea to wait until you have an answer you believe is correct. That way, the person who checks it will know you put some effort into it and that you are really close. Also, if you are having trouble with a specific problem, it might be helpful to include that problem in your post rather than just posting your entire solution. It helps people focus on what you are having trouble with. In summary, asking for help is okay as long as you have put in some effort and provide specific information about what you need help with.
calcdummy

## Homework Statement

For each of the following, identify the base function and describe the transformation(s):
f(x)=-4(3x)^2 + 5

## Homework Equations

f(x) = -4(3x)^2 + 5

## The Attempt at a Solution

Alright so my attempt at figuring out the requested answers are:

Base function = x^2
- has been shifted up 5 units
- has been vertically stretched by 3
- reflected in the x-axis by -4

At this moment I'm really confused on my answer. I have a feeling that there is more to it and that I got a couple of things wrong but I just can't figure out what... could someone please help me out?

calcdummy said:

## Homework Statement

For each of the following, identify the base function and describe the transformation(s):
f(x)=-4(3x)^2 + 5

## Homework Equations

f(x) = -4(3x)^2 + 5

## The Attempt at a Solution

Alright so my attempt at figuring out the requested answers are:

Base function = x^2
- has been shifted up 5 units
- has been vertically stretched by 3
- reflected in the x-axis by -4

At this moment I'm really confused on my answer. I have a feeling that there is more to it and that I got a couple of things wrong but I just can't figure out what... could someone please help me out?

Order might make a difference. If you start on the "inside" the order would be:
vertically stretched by 3 (maybe you would say by 32?)
reflected in the x-axis and vertically stretched by 4 (could be in either order)
shifted up 5 units.

LCKurtz said:
Order might make a difference. If you start on the "inside" the order would be:
vertically stretched by 3 (maybe you would say by 32?)
reflected in the x-axis and vertically stretched by 4 (could be in either order)
shifted up 5 units.

Yay, basically my answers are on point I just need to work on my arrangement in order for it to make better sense. I'll definitely work on that. Thank you for your time and help.

On a side note, do you know if it will be alright for me to make posts asking PF contributors to help me check my answers in the homework section or should I maintain to making posts only when I am in need of help?

calcdummy said:
On a side note, do you know if it will be alright for me to make posts asking PF contributors to help me check my answers in the homework section or should I maintain to making posts only when I am in need of help?

People often ask for others to look over their work. I don't think there is any problem with that.

## 1. What is a quadratic equation?

A quadratic equation is a mathematical expression in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It is a polynomial equation of degree 2, meaning that the highest power of the variable is 2.

## 2. How do you find the transformations of a quadratic equation?

To find the transformations of a quadratic equation, you need to first identify the vertex of the parabola. The vertex is the point where the parabola changes direction. Then, you can use the following transformations:

• Translation: The vertex is shifted horizontally or vertically by adding or subtracting a constant.
• Reflection: The parabola is reflected over the x-axis or y-axis.
• Dilation: The parabola is stretched or compressed horizontally or vertically by multiplying the constant.

## 3. How do you determine the base function of a quadratic equation?

The base function of a quadratic equation is the simplest form of the equation, where the coefficient of x^2 is 1. To determine the base function, divide all the terms of the equation by the coefficient of x^2. For example, if the equation is 2x^2 + 4x + 6 = 0, the base function would be x^2 + 2x + 3 = 0.

## 4. How do you graph a quadratic equation?

To graph a quadratic equation, first plot the vertex of the parabola. Then, use the transformations to determine the coordinates of two other points on the parabola. Plot these points and connect them to create a smooth curve. You can also use the axis of symmetry, which is a vertical line passing through the vertex, to find other points on the parabola.

## 5. What are the applications of quadratic equations?

Quadratic equations have numerous applications in various fields, including physics, engineering, finance, and computer science. They can be used to model the motion of objects, design bridges and buildings, calculate interest and growth rates, and create computer graphics and animations.

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