Answered

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MAKE YOUR OWN POLYNOMIAL FUNCTIONS. DRAW THE GRAPH OF IT IN A CLEAN SHEET OF PAPER.

HI! GOOD AFTERNOON CAN YOU PLS HELP ME WITH MY MATH PROBLEM HEHE​

MAKE YOUR OWN POLYNOMIAL FUNCTIONS DRAW THE GRAPH OF IT IN A CLEAN SHEET OF PAPERHI GOOD AFTERNOON CAN YOU PLS HELP ME WITH MY MATH PROBLEM HEHE class=

Sagot :

KAntoineDoix

✒️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]

  • [tex] y = 6 [/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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