Completing the square is a method that can be used to solve the quadratic equation x^2+6x+14 in the form of (x+a)^2+b. The way we find a and b is as follows:For constant a, is found by halving the coefficient of x, so that a=6/2 where a=3For constant b, is found by taking the constant at the end of the quadratic, +14, and subtracting a^2 from it,so that b=14 - a^2 =14 - (3)^2 = 14 - 9 = 5 Now , let a=3 and b=5 and we can substitute them in the form of (x+a)^2+b Thus, the result for completing the square is:x^2+6x+14=(x+3)^2+5 Finally, we can check if the answer is true by (i) making sure that when we expand the result is equal to the quadratic equation(ii) substituting x with a number(1,2,3,..etc) and the result should be equal in both sides, LHS=RHS e.g let x=1, x^2+6x+14=(x+3)^2+5 (1)^2+6(1)+14=(1+3)^2+5 21=21 Therefore, is true.

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Write x^2+6x+14 in the form of (x+a)^2+b where a and b are constants to be determined.

Given: 𝑓(𝑥) = 𝑎𝑥^3 + 𝑏𝑥^2 − 3 and 𝑓"(−2) = 0. If it is further given that the point (−3; 6) lies on the graph of 𝑓. Show that 𝑎 = 1/3 and 𝑏 = 2.

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