Respuesta :
Answer:
d) The equation of the standard parabola
x² = 6 y
Step-by-step explanation:
The given directrix is y= -31.5
The equation of the parabola is of the form x² =4 a y
Given focus (0,1.5) , Here a= 1.5
The equation of the standard parabola
x² = 4 a y
x² = 4 (1.5)y
x² = 6 y
Conclusion:-
The equation of the standard parabola
x² = 6 y
The equation that represents the parabola shown on the graph is x∧2 = 6 y
What is a parabola?
A parabola is known as a plane curve that starts from a point and moves such that its distance from a fixed point is equal to its distance from a fixed line.
The graph shows a vertical parabola opened upwards with the vertex at the origin.
How to determine the equation
The equation of the parabola from the graph is;
x∧2 = 4ay
The equation of the directrix;
y = -a = -1. 5
Thus, the value of a = 1.5
Then, substitute the value of a = 1.5 in the equation deduced from the graph
x∧2 = 4 × (1.5) × y
x∧2 = 6 y
Therefore, the equation that represents the parabola shown on the graph is x∧2 = 6 y
Learn more on parabola here:
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