Quadratics ?

[1123581321]

I was reading up on physics and came across a standard form quadratic equation. I know what a quadratic equation is but didnt know they had (a) standard form. So could someone please explain it to me...

Thanks.

[khaled]

Quadratic Equation: $a x^2 + b x = c$

 

where a, b, and c are constants, and $a \ne 0$

[Schrödinger's hat]

I've seen different conventions in different textbooks, the most common:

$y=f(x)=ax^2+bx+c$

Another (wiki calls this standard form) is:

$y=f(x)=a(x-x_0)^2+y_0$

 

This allows you to quickly draw the parabola that it represents as you just get a standard parabola $y=x^2$, scale it in the y direction by a factor of a, then place the turning point at

$(y_0,x_0)$

[mississippichem]

  On 3/7/2011 at 10:27 AM, 1123581321 said:

I was reading up on physics and came across a standard form quadratic equation. I know what a quadratic equation is but didnt know they had (a) standard form. So could someone please explain it to me...

Thanks.

 

It also allows you to pick out the quadratic formula easily, a method that always gives you a solution:

 

$x= \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$

[Schrödinger's hat]

To clarify what mississippichem said in case of confusion, the quadratic formula as he posted it applies to the first form I mentioned, when trying to find f(x)=y=0 or:

$ax^2+bx+c=0$

Note that this isn't the same as the form khaled posted, which is much less common.

[khaled]

  On 3/8/2011 at 2:38 PM, Schrödinger said:

I've seen different conventions in different textbooks, the most common:

$y=f(x)=ax^2+bx+c$

Another (wiki calls this standard form) is:

$y=f(x)=a(x-x_0)^2+y_0$

 

This allows you to quickly draw the parabola that it represents as you just get a standard parabola $y=x^2$, scale it in the y direction by a factor of a, then place the turning point at

$(y_0,x_0)$

 

that is not an Equation, that is a Function ...

[the tree]

[imath]f(x)[/imath] is a function, [imath]y=f(x)[/imath] is an equation.