What is the vertex of y=3x^2-24x+5?

To find that, we can put this into vertex form:

y = a(x - h)² + k

in this form, the vertex is (h, k)

So we have:

y = 3x² - 24x + 5

To do this, we need the right side in the form of (x² + bx), so starting with subtracting 5 from both sides and dividing both sides by 3:

y - 5 = 3x² - 24x
(y - 5) / 3 = x² - 8x

Now complete the square on the right side by adding 16 to both sides:

16 + (y - 5) / 3 = x² - 8x + 16

Now factor, then solve for y again:

16 + (y - 5) / 3 = (x - 4)²
(y - 5) / 3 = (x - 4)² - 16
y - 5 = 3(x - 4)² - 48
y = 3(x - 4)² - 43

so the vertex is (4, -43)

answer A.