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Chapter 16.2, part 1: Solving Quadratic Functions by Square Roots (Imaginary #s)
Solving Quadratic Equations by SQUARE ROOTS
*Square Root Property – To solve a quadratic equation, you can take the square root of both sides.*Don’t forget to consider the positive and negative square roots!
*Imaginary #'s are also referred to as complex numbers!
Completing the Square on the next page.
Chapter 16.2, part 2: Solving Quadratic Functions by
Completing the Square
Visual Method of Completing the Square:
How many 1-by-1 tiles will it take to
complete the square?
How many 1-by-1 tiles will it take to
complete the square?
How many 1-by-1 tiles will it take to
complete the square?
Below, we will answer different questions about the figures. We will also
represent the area of each figure with an
expression.
So, not only are we physically completing a square, we are also
completing a perfect square trinomial.
Because of the statement to the left, we can complete the square with any expression: x2 + bx.
We can do this by dividing b by 2, then squaring the number, this value becomes c.
Complete the square below:
We can compare the number of rectangular
tiles with the 1-by-1 tiles to discover a pattern.
The number a rectangular tiles in each figure corresponds to the coefficient of x, while the
number of 1-by-1 tiles corresponds to the constant.
The number a rectangular tiles in each figure corresponds to the coefficient of x, while the
number of 1-by-1 tiles corresponds to the constant.