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Re-write the quadratic function below in Standard Form: y=−6(x−1)(x−5)y= -6(x-1)(x-5)

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Full solution

Q. Re-write the quadratic function below in Standard Form: y=−6(x−1)(x−5)y= -6(x-1)(x-5)
  1. Expand Quadratic Function: Expand the quadratic function using the distributive property (FOIL method).\newliney=−6(x−1)(x−5)y = -6(x-1)(x-5)\newlineFirst, multiply the terms in the first set of parentheses by each term in the second set of parentheses.\newliney=−6[(x×x)+(x×−5)+(−1×x)+(−1×−5)]y = -6[(x \times x) + (x \times -5) + (-1 \times x) + (-1 \times -5)]
  2. Simplify Expression: Simplify the expression by combining like terms.\newliney=−6[x2−5x−x+5]y = -6[x^2 - 5x - x + 5]\newliney=−6[x2−6x+5]y = -6[x^2 - 6x + 5]
  3. Distribute −6-6: Distribute the −6-6 across each term inside the brackets.\newliney=−6×x2+6×6x−6×5y = -6 \times x^2 + 6 \times 6x - 6 \times 5
  4. Complete Multiplication: Complete the multiplication.\newliney=−6x2+36x−30y = -6x^2 + 36x - 30
  5. Write in Standard Form: Write the final expression in standard form.\newlineThe standard form of a quadratic function is ax2+bx+cax^2 + bx + c.\newlineTherefore, the standard form of the given quadratic function is y=−6x2+36x−30y = -6x^2 + 36x - 30.

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