A parabola has vertex (2,3) and contains the point (0,0). If this parabola is a function, what is its equation? Suppose this parabola is not a function, but is a "sleeping parabola, what is its equation?
+130536 In vertex form, we have :
y = a(x - 2)^2 + 3 and we know that (0, 0) is on the graph....so
0 = a(0 - 2)^2 + 3 simplify
0 = 4a + 3 → a = -3/4
So the equation of the first one is
y = -(3/4) (x - 2)^2 + 3
"Sleeping parabola" ....haven't heard that term used before......!!!!!
Anyway, we have
x = a(y - 3)^2 + 2 .and since (0, 0) is on the graph, we have
0 = a (0 - 3)^2 + 2
0 = 9a + 2 → a = -2/9
So the equation of the second is :
x = -(2/9)(y - 3)^2 + 2
Here are the graphs of each.....https://www.desmos.com/calculator/gk31k4magg
