In 10th grade, I learned that $ax^2 + bx + c$ is a quadratic function
I'm currently learning how to "investigate quadratic functions in vertex form" and in my textbook, they define $f(x) = x^2$ as the simplest form of a quadratic function. I don't understand how this is the simplest form of a quadratic function, was it derived from the first mentioned equation?
On
I didn't understand what your textbook means by stating "$f(x)=x^2$ is the simplest form of a quadratic function". The phrase simplest form is generally used when you have an expression but according to the concept, it is inappropriate to use that expression so you find it's simplest form in order to make things easier. If we give an example, say we are finding the roots of the equation $x^2+5x+6=0$, the simplest form of the polynomial on LHS is $(x+3)(x+2)$ because we are seeking the $x$ values that makes LHS$=0$ and it is easier to find them using the second expression. But for another concept, simplest form may be the expression $x^2+5x+6$.
I think what they mean by saying that is that $f(x)=x^2$ is a "simple" function to examplify the quadratic functions because as stated above, we have $a = 1$, $b=c=0$. But in my opinion, all of the quadratic functions with $b=c=0$, in other words $f(x) = ax^2$, can be thought as "simple" in real plane since these functions really look alike:
$f(x)=x^2$ is the simplest form because $a=1$ and $c=0$, it can't get any simpler than that. it's quadratic $x$ is raised to the second power.