Entry posted by Legolover-361
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Since I'm taking a math class, why should I not bring some educational value to this blog? Writing mathematical explanations will help me better understand the concepts and perhaps allow you readers to comprehend them with more ease, as well.
Note: This is a simple subject because I don't want to jump right into describing more complex things without working my way to that level first. I'm just learning pre-calculus, after all.
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Let's consider a typical quadratic equation, y = -x2 - 2x + 3. The resultant graph is an upside-down parabola: Its y-axis intercept is (0,3), and its x-intercepts are (-3, 0) and (1, 0). Using this graph, you can determine the values of y in relation to the values of x, but you can't determine other values.
Enter parametric equations. Let us use t as the parameter so f(t) = x and g(t) = y. We will further define t by saying x = 2t. Substituting x for 2t:
y = -(2t)2 - 2(2t) + 3
y = -4t2 - 4t + 3
Voila! We now have a system of two parametric equations that defines x and y in relation to the parameter t, which can represent whatever you choose.
The parameter can be removed in a similar fashion. Taking the above equations, x = 2t and y = -4t2 - 4t + 3, substitute x for 2t in the y equation:
y = -4t2 - 4t + 3
y = (-1)(2t)(2t) - 2(2t) + 3
y = -x2 - 2x + 3
(I'll add more info later.)
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