y=3(x-2)^2 +4 to standerd form

Answer 1

To convert the equation y=3(x-2)^2 +4 to standard form, we need to expand and simplify the equation.

First, we expand the square term using the formula (a-b)^2 = a^2 - 2ab + b^2:

y = 3(x-2)(x-2) + 4
y = 3(x^2 - 4x + 4) + 4
y = 3x^2 - 12x + 12 + 4
y = 3x^2 - 12x + 16

Now, we rewrite the equation in standard form by setting it equal to zero:

3x^2 - 12x + 16 = 0

So, the standard form of the equation y=3(x-2)^2 +4 is 3x^2 - 12x + 16 = 0.