in the function f(x)=4(x^2-6x+ )+20 what number will complete the square
I would multiply 4 in to get 4x^2-24x+20
Then factor out 4 4(x^2-6x+5)
Complete the square inside the bracket 4[(x-3)^2-9+5] = 4[(x-3)^2 -4]= 4(x-3)^2 -16
I would think it is +16 needed to complete the square
f(x) = 4(x^2 - 6x + 9 - 9) + 20
= 4( (x-3)^2 - 9) + 20
= 4(x-3)^2 - 36 + 20
= 4(x-3)^2 - 16
To complete the square in the function f(x) = 4(x^2 - 6x + ) + 20, we need to find the number that, when added to the expression inside the parentheses, will create a perfect square trinomial.
To find this number, we can follow these steps:
Step 1: Take half of the coefficient of the x-term and square it. In this case, the coefficient of the x-term is -6, so we have:
(-6/2)^2 = (-3)^2 = 9
Step 2: Add this number to the expression inside the parentheses.
(x^2 - 6x + 9)
Step 3: Rewrite the original equation by factoring the perfect square trinomial obtained in step 2.
f(x) = 4(x^2 - 6x + 9) + 20
Step 4: Simplify the equation by distributing the 4 to every term inside the parentheses.
f(x) = 4x^2 - 24x + 36 + 20
Simplifying further:
f(x) = 4x^2 - 24x + 56
Therefore, the number that completes the square in the given function is 9.