Answer:
[tex]y = (x-6) ^ 2 -16[/tex]
Step-by-step explanation:
The vertex form for a quadratic equation has the following form:
[tex]y = (x-h) ^ 2 + k[/tex]
Where the vertice of the equation is the point (h, k)
To transform the equation [tex]y = x ^ 2 -12x +20[/tex] in its vertex forms we must find its vertex.
Be a quadratic equation of the form:
[tex]ax ^ 2 + bx + c[/tex]
Where a, b and c are real numbers, then the vertex of the equation will be:
[tex]x = - \frac{b}{2a}[/tex]
For the given equation:
[tex]b = -12\\a = 1[/tex]
Therefore the vertice is:
[tex]x = - \frac{-12}{2(1)}\\\\x = 6[/tex]
Now we substitute x = 6 into the equation and find the value of k.
[tex]y = (6) ^ 2 -12 (6) +20\\\\y = -16 = k[/tex]
Therefore the vertice is: (6, -16)
And the equation is:
[tex]y = (x-6) ^ 2 -16[/tex]
