The equation for the parabola is (x - 2)² = 16(y + 1) if the vertex of the parabola is (2, -1) and focus of the parabola is (2, 3) option (D) is correct.
What is a parabola?
It is defined as the graph of a quadratic function that has something bowl-shaped.
We have:
The vertex of the parabola = (2, -1)
The focus of the parabola = (2, 3)
As we know, the vertex form of the parabola is given by:
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
(x - 2)² = 4a(y - (-1))
(x - 2)² = 4a(y + 1)
The value of a can be found using the formula:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
(c, d) = (2, 3)
a = √[(2-2)² + (3-(-1))²]
a = √ (3+1)²]
a = 4
(x - 2)² = 4(4)(y + 1)
(x - 2)² = 16(y + 1)
Thus, the equation for the parabola is (x - 2)² = 16(y + 1) if the vertex of the parabola is (2, -1) and focus of the parabola is (2, 3) option (D) is correct.
Learn more about the parabola here:
brainly.com/question/8708520
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