The equation of a parabola in vertex form is given by (y - k)² = 4a(x - h) if the parabola is horizontal, and (x - h)² = 4a(y - k) if the parabola is vertical. Here, (h, k) is the vertex of the parabola.

Given that the vertex of the parabola is at (4, -3), we can substitute h = 4 and k = -3 into the equations.

For a horizontal parabola, the equation becomes (y - (-3))² = 4a(x - 4), or (y + 3)² = 4a(x - 4).

For a vertical parabola, the equation becomes (x - 4)² = 4a(y - (-3)), or (x - 4)² = 4a(y + 3).

Looking at the answer choices, we can see that they are all in the form of a vertical parabola, but the coefficient of the squared term is -3, not 4a. This means that a = -3/4.

Substituting a = -3/4 into the equation for a vertical parabola, we get (x - 4)² = -3(y + 3), or x = -3(y + 3)² + 4.

Therefore, the correct answer is A. x = -3(y + 3)² + 4.

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The equation of a parabola in vertex form is given by (y - k)² = 4a(x - h) if the parabola is horizontal, and (x - h)² = 4a(y - k) if the parabola is vertical. Here, (h, k) is the vertex of the parabola.

Given that the vertex of the parabola is at (4, -3), we can substitute h = 4 and k = -3 into the equations.

For a horizontal parabola, the equation becomes (y - (-3))² = 4a(x - 4), or (y + 3)² = 4a(x - 4).

For a vertical parabola, the equation becomes (x - 4)² = 4a(y - (-3)), or (x - 4)² = 4a(y + 3).

Looking at the answer choices, we can see that they are all in the form of a vertical parabola, but the coefficient of the squared term is -3, not 4a. This means that a = -3/4.

Substituting a = -3/4 into the equation for a vertical parabola, we get (x - 4)² = -3(y + 3), or x = -3(y + 3)² + 4.

Therefore, the correct answer is A. x = -3(y + 3)² + 4.

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The equation of a parabola in vertex form is given by (y - k)² = 4a(x - h) if the parabola is horizontal, and (x - h)² = 4a(y - k) if the parabola is vertical. Here, (h, k) is the vertex of the parabola.

Given that the vertex of the parabola is at (4, -3), we can substitute h = 4 and k = -3 into the equations.

For a horizontal parabola, the equation becomes (y - (-3))² = 4a(x - 4), or (y + 3)² = 4a(x - 4).

For a vertical parabola, the equation becomes (x - 4)² = 4a(y - (-3)), or (x - 4)² = 4a(y + 3).

Looking at the answer choices, we can see that they are all in the form of a vertical parabola, but the coefficient of the squared term is -3, not 4a. This means that a = -3/4.

Substituting a = -3/4 into the equation for a vertical parabola, we get (x - 4)² = -3(y + 3), or x = -3(y + 3)² + 4.

Therefore, the correct answer is A. x = -3(y + 3)² + 4.

The vertex of this parabola is at (4, -3). Which of the following could be its equation?A.x = -3(y + 3)2 + 4B.x = -3(y - 4)2 - 3C.x = -3(y + 4)2 - 3D.x = -3(y - 3)2 + 4SUBMITarrow_backPREVIOUS

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