Question

The graph of the parabola

y = 3(x + 4)2 + 2 has vertex (-4, 2).
If this parabola is shifted 5 units
down and 3 units to the right,
what is the equation of the new
Parabola?

Answer 1

To find the new equation of the parabola after shifting it down by 5 units and to the right by 3 units, we adjust the vertex coordinates and apply these changes to the vertex form of the original equation. The new parabolic equation is y = 3(x + 1)^2 - 3.

Step-by-step explanation:

To find the equation of the new parabola after shifting the original parabola y = 3(x + 4)2 + 2 down by 5 units and to the right by 3 units, we apply a horizontal and vertical translation to the vertex form of the parabola.

The original vertex is (-4, 2). Shifting the vertex 3 units to the right will make the new x-coordinate of the vertex -4 + 3 = -1. Shifting the vertex 5 units down will make the new y-coordinate of the vertex 2 - 5 = -3. Therefore, the new vertex is (-1, -3).

Substituting the new vertex into the vertex form, we get the new equation:

y = 3(x + 1)2 - 3

Answer 2

The equation of the new parabola after shifting down and to the right is y = 3(x + 1)^2 - 3.

Step-by-step explanation:

The equation of the parabola after shifting down and to the right:

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

Given that the original parabola has a vertex of (-4, 2), after shifting 5 units down and 3 units to the right, the new vertex will be (h + 3, k - 5).

Therefore, the equation of the new parabola is y = 3(x + 1)^2 - 3.