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By Chuang C.T. (ed.)

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If even one sign is different, then the equation is not x-symmetric. Origin-symmetry is achieved when the graph does exactly the opposite thing on either side of the origin. 4, notice that the origin-symmetric curve snakes down and to the right as x gets more positive, and up and to the left as x gets more negative. In fact, every turn in the second quadrant is matched and inverted in the fourth quadrant. To test an equation for origin-symmetry, replace all x’s with (–x) and all y’s with (–y). Once again, if the simplified equation matches your original equation, then that function is originsymmetric.

Because there is no upper bound, you write infinity. If infinity is one of the boundaries, you always use a parenthesis next to it. Kelley’s Cautions If your instructor demands one answer per equation, eliminate all of your solutions except for the one (and there will only be one) that falls into the appropriate range. That range is ␲ < < ␲ for sine, tangent, 2 2 and cosecant; for cosine, cotangent, and secant, use the interval of 0 ≤ θ ≤ π. Each of my examples will ask for the solution to the trigonometric equation on the interval [0, 2π).

24 Part 1: The Roots of Calculus Example 8: Solve the equation 2x2 + 12x – 18 = 0, this time using the quadratic formula. Solution: Because the equation is already set equal to 0, it is in form ax2 + bx + c = 0, and a = 2, b = 12, and c = –18. Plug these values into the quadratic formula and simplify: So although there are fewer steps to the quadratic formula, there is some room for error during computation. You should practice both methods, but primarily use the one that feels more comfortable to you.

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