The vertex of this parabola is at (1,3). Which of the following could be its equation?

A. y = 3(x + 1)2-3
B. x = 3(y-3)2 + 1
C. y = 3(x + 1)2 + 3
D. x= 3(y - 3)2-1

The basic equation for a y = x-squared parabola is

y=a(x-h)^2+ky=a(x−h)

2

+k so using the info given, our equation would have to be:

y=3(x-1)^2+3y=3(x−1)

2

+3 and that is not one of our options. No worries, we have another option.

The basic equation for an x = y-squared parabola is

x=a(y-k)^2+hx=a(y−k)

2

+h so using the info given, our equation would have to be:

x=3(y-3)^2+1x=3(y−3)

2

+1 which is option C.

the forst and 3rd

step-by-step explanation:

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!