Transformations of a **quadratic** equation, narrowing or expanding a **parabola** by changing the leading coefficient, vertical transformations by adding or subtracting a constant term, comparing the width of two parabolas by using the absolute value of the leading coefficient, and comparing a transform **parabola** with theirs

Similarly, you may be wondering what is the transform of a **quadratic function**?

Transform of **quadratic functions**. The antiderivative of the square is f(x)=x2. In vertex form it would be f(x)=1(x-0)2+0, where a=1, h=0 and k=0. The **graph** peaks at (0,0) and opens. By changing the value of a, h and k, which are called parameters, you can create a transformation of the **function**.

What are the 4 types of transformations?

Es There are four main types of transformations: translation, rotation, reflection, and dilation.

Considering what are the rules for transformations for graphing **quadratic functions** with parabolas?

Draw the **function** y= −12(x−3)2+2 . If we start with y=x2 and replace x with x−3, this **shifts** the **graph** 3 units to the right. If we then multiply the right-hand side by −12, the **parabola** is turned upside down and vertically compressed (or “squashed”) by a factor of 2.

How do you describe a **quadratic** equation?

A **quadratic** equation is a **quadratic** equation, which means it contains at least one term squared. The standard form is ax² + bx + c = 0, where a, b, and c are constants or numeric coefficients, and x is an unknown variable. An absolute rule is that the first constant “a” must not be zero.

## How to shift a function?

– The equation y = f(x + c) **shifts** the Graph of y = f(x) to the left **c units**. (Adding a constant inside the **function shifts** the **graph** to the left.) – The equation y = f(x − c) **shifts** the **graph** of y = f(x) to the right by **c units**. (Subtracting a constant within the **function shifts** the **graph** to the right.)

## How do you find the transform of a function?

Here are some things we can do:

- Move 2 spaces up: h(x) = 1/x + 2.
- Move 3 spaces down: h(x) = 1/x − 3.
- Move 4 squares right:h(x) = 1/(x−4)
**graph**. - Move 5 spaces to left:h(x) = 1/(x+5)
- Extend it 2 in y-direction: h(x) = 2/x.
- Compress it by 3 in x-direction: h(x) = 1/(3x)
- Turn it upside down: h(x) = −1/x.

## How do you find a vertical asymptote?

To find the vertical asymptote (s) of a rational **function**, simply set the denominator to 0 and solve for x. We need to set the denominator to 0 and solve: The easiest way to solve this square is to factor the trinomial and set the factors to 0. There are vertical asymptotes at .

## How do you know if a parabola is stretched or compressed?

- If a>1 display style a>1 a>1, then the
**graph**will be stretched. - If 0graph will be compressed.
- If a<0 drawing style is a<0 a<0, then there will be a combination of a vertical stretch or compression with a vertical reflection.

## WHAT IS A in vertex form?

The vertex form of a square is given by. y = a(x – h) 2 + k, where (h, k) is the vertex. The “a” in vertex form is the same “a” as. in y = ax 2 + bx + c (i.e. both a have exactly the same value). The sign on “a” tells you if the squares open up or open down.

## How to graph a shifted parabola?

Has the **function** y=x2+b a **graph** that looks just like the standard **parabola** with the vertex shifted **b units** along the y-axis. So the vertex is at (0,b). When b is positive the **parabola** moves up and when b is negative it moves down. Similarly, we can move the **parabola** horizontally.

## How do you identify the domain and range of a function?

Another way to identify the domain and range of **functions** is the use of charts. Since the domain refers to the set of possible input values, the domain of a chart consists of all the input values displayed on the x-axis. The range is the set of possible output values shown on the y-axis.

## How do you find asymptotes?

The horizontal asymptote of a rational **function** can be found by looking at the Degrees of numerator and denominator.

- Numerator degree is less than denominator degree: horizontal asymptote at y = 0.
- Numerator degree is one greater than denominator degree: no horizontal asymptote; skewed asymptotes.

## How to find transformations?

The **function** translation / transformation rules:

- f (x) + b
**shifts**the**function b units**up. - f (x) – b
**shifts**the**function b units**down. - f (x + b)
**shifts**the**function b units**left. - f (x – b)
**shifts**the**function b units**to the right. - -f (x) mirrors the
**function**on the x-axis (i.e. upside down).

## How to shift a quadratic function horizontally?

You can plot a horizontal (left, right) shift of the **graph** of f(x) =x2 f ( x ) = x 2 by adding or subtracting a constant h from the variable x before squaring. If h>0 , the **graph shifts** to the right and if h<0 , the **graph shifts** to the left.