Question

7. Rewrite each relation in the form

y = a(x = h)^2 + k by completing
the square.

c) y = 3x^2+ 90x + 50

Please show the steps

Answer 1

y = 3(x + 15)^2 - 625

Explanation:

y = 3x^2 + 90x + 50

To complete the square, the coefficient of the x^2 term must be 1. We have 3x^2, so we factor out a 3 from the first two terms.

y = (3x^2 + 90x) + 50

y = 3(x^2 + 30x) + 50

To complete the square, square half of the coefficient of the x term. The x term is 30x. Half of 30 is 15. 15 squared is 225.

Since you are adding 225 inside the parentheses, and the quantity in parentheses is being multiplied by 3, you have really added 3 * 225 = 675 to the polynomial, so you must subtract 675 from the polynomial to keep it equal.

y = 3(x^2 + 30x + 225) + 50 - 675

Now we change the trinomial which is perfect square into the square of a binomial.

y = 3(x + 15)^2 - 625