✒️POLYNOMIAL
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[tex] \large\underline{\mathbb{DIRECTIONS}:} [/tex]
- Make your own polynomial function. Draw the graph of it in a clean sheet of paper.
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[tex] \large\underline{\mathbb{ANSWER}:} [/tex]
[tex] \qquad \Large \:\:\rm{y = x^3 - 4x^2 + x + 6} [/tex]
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[tex] \large\underline{\mathbb{SOLUTION}:} [/tex]
» Choose any x-intercepts. (I chose three of them for cubic function).
- [tex] x = 3\:, \quad x = \text-1 \:, \quad x = 2 [/tex]
» Equate them to zero then multiply them equal to zero.
- [tex] x - 3 = 0\:, \quad x + 1 = 0 \:, \quad x - 2 = 0 [/tex]
- [tex] 0 = (x - 3)(x + 1)(x - 2) [/tex]
» The given equation gives the x-intercept of the fuction. Set zero to y to get the function.
- [tex] y = (x - 3)(x + 1)(x - 2) [/tex]
» Find the y intercept of the function (set x to zero)
- [tex] y = (0 - 3)(0 + 1)(0 - 2) [/tex]
- [tex] y = (\text- 3)(1)(\text- 2) [/tex]
» Thus, the y intercept is 6. Now that we have the given, plot the points where the graph passes through.
- x-intercepts = (3, 0), (-1, 0), (2, 0)
- y-intercept = (0, 6)
» After plotting, know its end behavior using the leading coefficient test.
- [tex] y = (x - 3)(x + 1)(x - 2) [/tex]
- [tex] y = (x^2 - 2x - 3)(x - 2) [/tex]
- [tex] y = x^3 - 4x^2 + x + 6 [/tex]
» Since the leading coefficient is positive and its degree is odd, then the graph will fall to the left and rises to the right.
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(ノ^_^)ノ
