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MPM2D IN 4.1 Unit #4 Quadratic Functions Name: Date: Characteristics of Quadratics For each of the following quadratic functions, complete the tables of values (To). Make a sketch of the quadratic.
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How to fill out characteristics of quadratics

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How to fill out characteristics of quadratics:

01
Identify the general form: The general form of a quadratic equation is ax^2 + bx + c = 0. To fill out the characteristics, you first need to identify the values of a, b, and c in the equation.
02
Determine the vertex: The vertex is a crucial characteristic of a quadratic equation. To find the vertex, you can use the formula x = -b / (2a) to determine the x-coordinate, and then substitute it into the equation to find the corresponding y-coordinate.
03
Calculate the axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex. The formula to find the axis of symmetry is x = -b / (2a).
04
Find the y-intercept: The y-intercept is the point where the graph of the quadratic equation intersects the y-axis. To find the y-intercept, substitute x = 0 into the equation and solve for y.
05
Determine the x-intercepts: The x-intercepts (also known as roots or zeros) are the points where the graph of the quadratic equation intersects the x-axis. To find the x-intercepts, set y = 0 in the equation and solve for x using factoring, completing the square, or the quadratic formula.
06
Graph the quadratic equation: Once you have identified all the characteristics of the quadratic equation, plot the vertex, y-intercept, and x-intercepts on a coordinate plane to graph the equation.

Who needs characteristics of quadratics:

01
Mathematics students: Characteristics of quadratics are essential for algebra and calculus courses, and understanding them is fundamental to solving and graphing quadratic equations.
02
Engineers and scientists: Quadratic equations are widely used in various fields, including engineering and science. Understanding the characteristics of quadratics helps professionals in these disciplines model physical phenomena, optimize designs, and analyze data.
03
Financial analysts: Quadratic equations have applications in finance, such as determining the maximum profit or minimum cost for a business. Understanding the characteristics of quadratics allows financial analysts to make informed decisions and analyze trends in financial data.
04
Architects and designers: Quadratic equations are used in architecture and design to create aesthetically pleasing structures and objects. By understanding the characteristics of quadratics, architects and designers can manipulate shapes and curves to achieve desired outcomes.
In conclusion, learning how to fill out the characteristics of quadratics is crucial for those studying mathematics, as well as for professionals in various fields such as engineering, science, finance, architecture, and design.
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The characteristics of quadratics include the vertex, axis of symmetry, roots, y-intercept, and direction of opening.
Math students and researchers studying quadratic equations are required to analyze and report characteristics of quadratics.
Characteristics of quadratics can be filled out by determining the values of the vertex, axis of symmetry, roots, and y-intercept based on the given quadratic equation.
The purpose of characteristics of quadratics is to understand the behavior and properties of quadratic functions, and analyze their graphical representation.
Information such as vertex coordinates, axis of symmetry equation, roots, y-intercept, and direction of opening must be reported on characteristics of quadratics.
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