determine the maximum or minimum value of each of the following quadratic functions by completing the square. state the value of X corresponding with the maximum or minimum value

1. f(x)= x(square) - 6x + 2

2. f(x)= 3x(square) + 9x + 7

3. f(x)= 1 - 4x - x(square)

answer with solution plz.. "x(square) is x2" the digit 2 is too big

2. Originally Posted by callisto200
determine the maximum or minimum value of each of the following quadratic functions by completing the square. state the value of X corresponding with the maximum or minimum value

1. f(x)= x(square) - 6x + 2

2. f(x)= 3x(square) + 9x + 7

3. f(x)= 1 - 4x - x(square)

answer with solution plz.. "x(square) is x2" the digit 2 is too big
I'll do the first question to show you what you should do. Please publish your work so we have a chance to help you more specifically:

$f(x)=x^2-6x+2$

Consider $x^2-6x$ as the beginning of a complete square where the final square number is missing. If you have $ax^2 +bx$ then the final square is $\left(\dfrac b{2a}\right)^2$ . In your case a = 1. Thus the final number is $\left(\dfrac6{2}\right)^2 = 9$.

If you add 9 to get a complete square you must subtract the 9 at once so that the equation is still true:

$f(x)=x^2-6x\bold{\color{red}+9}\bold{\color{red}-9}+2$

Now collect the first 3 summands:

$f(x)=(x-3)^2-7$

The equation belongs to a parabola opening up. Thus the vertex is the minimum point. At x = 3 the function has ist smallest value f(3) = -7