1123581321 Posted March 7, 2011 Posted March 7, 2011 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 Posted March 8, 2011 Posted March 8, 2011 Quadratic Equation: [math]a x^2 + b x = c[/math] where a, b, and c are constants, and [math]a \ne 0[/math]
Schrödinger's hat Posted March 8, 2011 Posted March 8, 2011 I've seen different conventions in different textbooks, the most common: [math]y=f(x)=ax^2+bx+c[/math] Another (wiki calls this standard form) is: [math]y=f(x)=a(x-x_0)^2+y_0[/math] This allows you to quickly draw the parabola that it represents as you just get a standard parabola [math]y=x^2[/math], scale it in the y direction by a factor of a, then place the turning point at [math](y_0,x_0)[/math]
mississippichem Posted March 8, 2011 Posted March 8, 2011 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: [math] x= \frac{-b\pm\sqrt{b^{2}-4ac}}{2a} [/math]
Schrödinger's hat Posted March 8, 2011 Posted March 8, 2011 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: [math]ax^2+bx+c=0[/math] Note that this isn't the same as the form khaled posted, which is much less common.
khaled Posted March 9, 2011 Posted March 9, 2011 I've seen different conventions in different textbooks, the most common: [math]y=f(x)=ax^2+bx+c[/math] Another (wiki calls this standard form) is: [math]y=f(x)=a(x-x_0)^2+y_0[/math] This allows you to quickly draw the parabola that it represents as you just get a standard parabola [math]y=x^2[/math], scale it in the y direction by a factor of a, then place the turning point at [math](y_0,x_0)[/math] that is not an Equation, that is a Function ...
the tree Posted March 9, 2011 Posted March 9, 2011 [imath]f(x)[/imath] is a function, [imath]y=f(x)[/imath] is an equation. 1
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