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Name: Date: Period: Transformation of Quadratic Functions1. Write the vertex form of a quadratic function.2. Being specific, name 3 ways that a parabola changes with different types of “a value.3.
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How to fill out transformation of quadratic functions

01
To fill out the transformation of quadratic functions, follow these steps:
02
Identify the original quadratic function in the form: y = ax^2 + bx + c
03
Determine the values of 'a', 'b', and 'c' from the original function.
04
Calculate the vertex of the parabola using the formula: vertex_x = -b / (2a) and vertex_y = f(vertex_x)
05
Identify the axis of symmetry, which is a vertical line passing through the vertex (vertex_x).
06
Determine if the parabola opens upwards (a > 0) or downwards (a < 0).
07
Find the y-intercept by substituting x = 0 into the original quadratic function.
08
Determine if the parabola is wider or narrower than the original (|a| > 1 indicates narrower, |a| < 1 indicates wider).
09
Identify if the parabola shifted left or right by comparing the vertex_x value to 0. A negative value indicates a shift to the right, while a positive value indicates a shift to the left.
10
Determine if the parabola shifted up or down by comparing the vertex_y value to 0. A positive value indicates a shift upward, while a negative value indicates a shift downward.
11
Use the information gathered to write the transformed quadratic function in the form: y = a(x - h)^2 + k, where (h, k) represents the vertex coordinates.

Who needs transformation of quadratic functions?

01
Several groups of people may need to understand the transformation of quadratic functions, including:
02
- Students studying algebra, calculus, or any other mathematics course that covers quadratic functions.
03
- Engineers and scientists analyzing data that can be represented by parabolic curves.
04
- Architects and construction professionals working with parabolic shapes for design purposes.
05
- Computer programmers and data analysts using quadratic functions in software development or data modeling.
06
- Financial analysts and economists evaluating business or economic data with quadratic relationships.
07
- Any individual interested in understanding and analyzing parabolic curves and their transformations.

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Transformation of quadratic functions involves changing the shape, position, or size of the graph of a quadratic function.
Students or professionals studying quadratic functions are required to understand and apply transformations.
To fill out transformation of quadratic functions, one needs to identify the key components of the quadratic function and understand how different transformations affect its graph.
The purpose of transformation of quadratic functions is to analyze how various changes impact the appearance of the graph and to make predictions about the behavior of the function.
The information reported on transformation of quadratic functions typically includes the original function, the type of transformation applied, and the resulting graph.
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