The vertex of this parabola is at (1, 3). Which of the following could be its equation?A.x = 3(y - 3)2 - 1B.y = 3(x + 1)2 + 3C.y = 3(x + 1)2 - 3D.x = 3(y - 3)2 + 1SUBMITarrow_backPREVIOUS

The vertex form of a parabola is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Given that the vertex of the parabola is at (1, 3), we can substitute h = 1 and k = 3 into the vertex form of the parabola.

This gives us y = a(x - 1)² + 3.

Looking at the options, the equation that matches this form is:

C. y = 3(x + 1)² - 3

However, this equation is not exactly the same as our derived equation. The sign before the 1 in the bracket is different. In the standard form, it should be (x - 1), but in option C, it is (x + 1).

So, none of the given options is the correct equation for a parabola with a vertex at (1, 3).

The vertex form of a parabola's equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Given that the vertex of the parabola is at (1, 3), we can substitute h = 1 and k = 3 into the vertex form equation. This gives us y = a(x - 1)² + 3.

Comparing this with the given options, we can see that option B: y = 3(x + 1)² + 3 does not match because the sign before 1 should be negative (x - 1) not positive (x + 1).

Option C: y = 3(x + 1)² - 3 also does not match because the sign before 1 should be negative (x - 1) not positive (x + 1), and the constant term should be +3 not -3.

Option D: x = 3(y - 3)² + 1 is not in the correct form. The standard form is y = a(x - h)² + k, not x = a(y - h)² + k.

Option A: x = 3(y - 3)² - 1 is also not in the correct form. The standard form is y = a(x - h)² + k, not x = a(y - h)² + k.

Therefore, none of the given options could be the equation of the parabola with vertex at (1, 3).