Put this equation y=3x^2-12x+17 in the form 4a(x-h)=(y-k)^2
To put the equation y = 3x^2 - 12x + 17 in the form 4a(x-h)=(y-k)^2, we will first need to complete the square in order to write it in vertex form.
y = 3x^2 - 12x + 17
y = 3(x^2 - 4x) + 17
To complete the square, we need to take half of the coefficient of the x-term, square it, and add it to both sides of the equation:
y = 3(x^2 - 4x + 4) - 12 + 17
y = 3(x - 2)^2 + 5
Now, we can rewrite the equation in the desired form:
y = 3(x - 2)^2 + 5
y = 3(1)(x - 2)^2 + 5
Comparing it to the form 4a(x - h) = (y - k)^2, we can see that
a = 1, h = 2, and k = 5.
Therefore, the equation y = 3x^2 - 12x + 17 in the form 4a(x-h) = (y-k)^2 is:
4(1)(x-2) = (y-5)^2