From: Andrew Lorimer <andrew@lorimer.id.au> Date: Thu, 18 Apr 2019 07:00:07 +0000 (+1000) Subject: [methods] clarify cubic points of inflection X-Git-Tag: yr12~166 X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/d2489a663e3d71f28dbcab7094f8bfed7cc75fb6 [methods] clarify cubic points of inflection --- diff --git a/methods/polynomials.md b/methods/polynomials.md index a2fe7b3..afd4eab 100644 --- a/methods/polynomials.md +++ b/methods/polynomials.md @@ -36,12 +36,12 @@ Distance: $\vec{AB} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ ## Cubic graphs -$$y=a(x-b)^3 + c$$ +$$y=a(bx-h)^3 + c$$ -- $m=0$ at *stationary point of inflection* +- $m=0$ at *stationary point of inflection* (i.e. ({h \over b}, k)$) - in form $y=(x-a)^2(x-b)$, local max at $x=a$, local min at $x=b$ - in form $y=a(x-b)(x-c)(x-d)$: $x$-intercepts at $b, c, d$ - +- in form $y=a(x-b)^2(x-c)$, touches $x$-axis at $b$, intercept at $c$ ## Quartic graphs @@ -91,4 +91,4 @@ a_3 x + b_3 y + c_3 z = d_3\protect\end{cases}$ - Generate two new equations with only two variables - Rearrange & solve - Substitute one variable into another equation to find another variable -- etc. \ No newline at end of file +- etc.