Proof of Quadratic Theorem
Written below is the proof of the quadratic theorem:
Quadratics are of the form
The roots or zeros of the quadratic are the values in which we can input as the value in the function to output . The possible values that go into a function is referred to as the domain, and the possible values that come out of a function are referred to as the range. Be cautious to not confuse this word with the term range in a set of data, or the absolute difference between the greatest and least terms of a set.
Here is the proof of how to find the roots of a quadratic:
$ax^2+bx+c=0
a(x^2+\frac{b}{a}x)+c=0$ (Error compiling LaTeX. Unknown error_msg)
At this point, we use a method called completing the square.
$a(x^2+\frac{b}{a}x)=-c
a(x+\brac{b}{2a})^2=-c+\frac{b}{4a}
(x+\frac{b}{2a})^2=\frac{-c}{a}+\frac{b}{4a^2}
(x+\frac{b}{2a})^2=\frac{b^2-4ac}{4a^2}
x+\frac{b}{2a}=\frac{\pm(b^2-4ac)}{2a}
x=\frac{-b\pm(b^2-4ac)}{2a}$ (Error compiling LaTeX. Unknown error_msg)