We can answer this in two ways: Differentiation and Graphing.
<u>Differentitate:</u>
The first derivative of a function yields a function that provides the slope for any point on the line of the original function. The slope of a vertex is zero, so we can set the first derivative to 0 and solve for x.
f(x) = 3(x-1)^2 + 4
f(x) = 3(x-1)(x-1) + 4
f(x) = 3(x^2 - 2x + 1) + 4
f(x) = 3x^2 - 6x + 7
f'(x) = 6x -6
Set this = 0 and find x:
0 = 6x -6
x = 1
The value of y when x=1 in the original equation is:
f(1) = 3(1-1)^2 + 4
y = 4
The vertex is (1,4)
<u>Graph:</u>
You can use DESMOS to plot the function. The result is attached. Look for the vertex and read the coordinates. (1,4) seems to work.
Here is your answer they forgot to add the 3 in front this is your answer: -3.7+-0.25=-3.95 so as I'm look they added wrong its most like the 25 and the 7 were added wrong.
If we want to has 100 in the denominator we have to divide numerator and denominator by 2. Then total value of fraction doesnt change. Now read the fraction, its 23 hundreds, now just write as decimal, so, 0.23