What is a quadratic equation and what is its simplified and cannonic form?
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$\begingroup$Quadratics are usually written in the following three ways:
Expanded form
This form is written canonically as
$$f(x)=ax^2+bx+c$$
This is a very general form and it is easy to find $f(0)$ if needed. However, finding the roots are a bit more difficult.
Factored form
This form is written as
$$f(x)=a(x-x_1)(x-x_2)$$
This form is very convenient if you need the roots of $f(x)$, as they are simply $x_1$ and $x_2$.
Vertex Form (complete the square)
This form is written as
$$f(x)=a(x-h)^2+k$$
This form is convenient for finding the vertex $(h, k)$. This is the form that is used to derive the quadratic formula.
Expanded form is usually considered to be the most basic form, so this is probably what you want.
$\endgroup$ $\begingroup$A quadratic equation (in one variable) is a polynomial equation $P(x)=0$, where $P(x)$ is a polynomial of degree 2.
The canonical form of a quadratic equation is $ax^2+bx+c=0$. The simplified form I'm not sure about, but I'm guessing $x^2+bx+c=0$ (obtained from canonical by dividing both sides by the coefficient of $x^2$).
$\endgroup$ 2 $\begingroup$A quadratic equation is, in laymen's terms, a "curve". However, there is much more to it than that. Each quadratic has a degree(the highest power), a leading coefficient(the first coefficient), and a constant(the number without a variable). Quadratic equations can be factored in several ways. This is the AC method:
ax^2 + bx + c = d -> factors of ac that add to b -> ax^2 + f_1(b)x + f_2(b)x + c = d where f_1 is factor 1 and f_2 is factor two -> gcf(ax^2 + f_1(b)x)•(gx + h) + gcf(f_2(b)x + c)•(gx + h) = d -> At this point ax + b = bx + c, they should read the same. (gcf(ax^2 + f_1(b)x)+gcf(f_2(b)x + c))(gx + h) = dIn Algebra, Equation with the highest degree 2 is a quadratic equation. And its simplest form is $$ ax^2+bx+cx = 0, $$ where $x$ represents variable and $a$,$b$, and $c$ represents constant or numbers. Also, $a$ should not be equals to zero because if $a = 0$ then the equation will become a linear one. And its graphical representation is a parabolic shape.
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