The standard equation of the parabola is y = - (1 / 4) · (x + 2)² - 2. (Correct choice: C)
What is the equation of the parabola associated to a graph?
Herein we have information about the directrix and the vertex of the parabola. The formula for the standard form of the equation of the parabola is:
y - k = [1 / (4 · p)] · (x - h)² (1)
Where:
- p - Distance from the vertex to the focus.
- (h, k) - Coordinates of the vertex.
Please notice that the equation of the vertex is x = h - p. Then, if we know that p = - 1 and (h, k) = (- 2, - 2), then the equation of the parabola is:
y + 2 = - (1 / 4) · (x + 2)²
y = - (1 / 4) · (x + 2)² - 2
The standard equation of the parabola is y = - (1 / 4) · (x + 2)² - 2. (Correct choice: C)
To learn more on parabolas: https://brainly.com/question/21685473
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