The standard equations of the parabolas are listed below:
- y + 6 = - (1/14) · (x + 6)²
- y = (1/2) · (x + 4.5)²
- y - 5 = - (1/8) · (x - 2)²
- y + 5 = (1/4) · (x + 2)²
How to determine the standard equation of the parabola
In this question we have four case of parabolas with vertical axes of reference, whose standard formula is:
[tex]y - k = \frac{1}{4\cdot p}\cdot (x-h)^{2}[/tex] (1)
Where:
- (h, k) - The vertex of the parabola.
- p - Least distance between the vertex and the focus of the parabola.
Please notice that p < 0 when the directrix is above the focus, otherwise p < 0. The vertex is the midpoint of line segment between the directrix and the focus.
Now we proceed to derive the standard equations of the parabola:
1) Vertex:
(h, k) = 0.5 · (- 6, 4) + 0.5 · (- 6, - 3)
(h, k) = (- 6, 0.5)
Least distance:
p = - 3.5
y + 6 = - (1/14) · (x + 6)²
2) Vertex:
(h, k) = 0.5 · (0, - 4) + 0.5 · (0, - 5)
(h, k) = (0, - 4.5)
Least distance:
p = 0.5
y = (1/2) · (x + 4.5)²
3) Vertex:
(h, k) = 0.5 · (2, 3) + 0.5 · (2, 7)
(h, k) = (2, 5)
Least distance:
p = 2
y - 5 = - (1/8) · (x - 2)²
4) Vertex:
(h, k) = 0.5 · (- 2, - 6) + 0.5 · (- 2, - 4)
(h, k) = (- 2, - 5)
Least distance:
p = 1
y + 5 = (1/4) · (x + 2)²
To learn more on parabolas: https://brainly.com/question/4074088
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