Exam (elaborations)

Mathematic ultimate formula sheet for quadratics

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Course
MCR3U

Institution
11th Grade

This ultimate formula sheet provides a comprehensive overview of essential concepts, properties, and applications of quadratic functions. It is designed to assist high school students in mastering the fundamentals of quadratic equations while also serving as a valuable resource for university-level...

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Uploaded on October 17, 2024
Number of pages 2
Written in 2024/2025
Type Exam (elaborations)
Contains Only questions

Institution Secondary school
Education 11th Grade
Course MCR3U
School year 3

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MCR3U - Formula Sheet

1. Functions
• A function f is a relation that assigns to each element x in a set A exactly one element
y in a set B. This is denoted as f : A → B.
• Domain: The set of all possible input values (x-values).
• Range: The set of all possible output values (y-values).
• Vertical Line Test: If a vertical line intersects the graph of the relation at more than one
point, it is not a function.

2. Quadratic Functions
Standard Form
f (x) = ax2 + bx + c

Vertex Form
f (x) = a(x − h)2 + k (where (h, k) is the vertex)

Factored Form
f (x) = a(x − r1 )(x − r2 ) (where r1 and r2 are the roots)

Vertex
b
h=− , k = f (h)
2a

Axis of Symmetry
x=h

Minimum/Maximum Value
- If a > 0: Minimum value at k. - If a < 0: Maximum value at k.

Quadratic Formula
To find the roots of ax2 + bx + c = 0:
√
−b ± b2 − 4ac
x=
2a
1

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