Combine y-0.25(x-6.5)^2-20

Problem

y−0.25*(x−6.5)^2−20

Solution

1. Expand the squared binomial (x−6.5)^2 using the identity (a−b)^2=a^2−2*a*b+b^2

(x−6.5)^2=x^2−13*x+42.25

2. Distribute the coefficient −0.25 to each term inside the parentheses.

−0.25*(x^2−13*x+42.25)=−0.25*x^2+3.25*x−10.5625

3. Combine the constant terms −10.5625 and −20 to simplify the expression.

−10.5625−20=−30.5625

4. Rewrite the final expression by grouping all terms together.

y−0.25*x^2+3.25*x−30.5625

Final Answer

y−0.25*(x−6.5)^2−20=y−0.25*x^2+3.25*x−30.5625

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