Can someone explain to me how to find the vertex form of this equation?y= -x^2 + 12x-4Do i use the -b/2a formula? I just need this to be explained better biased on a equation i need to solve.

Accepted Solution

The quadratic equation has the general formula:
y = ax^2 + bx + c
The vertex form has the general formula:
y = a(x-h)^2 + k

To get the vertex formula, we will need to get the values of a,h and k as follows:
1- The value of a:
The value of "a" in the vertex form is the same as the value of "a" in the quadratic form
Therefore: a = -1
2- The value of h:
the value of "h" can be computed using the formula:Β 
h = -b / 2a
From the given quadratic equation: b = 12 and a = -1
Therefore: h = -12 / 2(-1) = 12/2 = 6
3- The value of k:
The value of k can be computed easily by evaluating y at the calculated h as follows:
The given equation is: y = -x^2 + 12x - 4
Compute the result at x=h=6 to get k as follows:
k = y = -(6)^2 + 12(6) - 4 = 32

Therefore, based on the above calculations, the vertex form would be:
y = a(x-h)^2 + k
y = -(x-6)^2 + 32