The vertex of this parabola is at (2, -1). When the y-value is 0, the x-value is 5. What is the equation of the parabola?
+23245 A formula for a parabola is: y - k = a(x - h)2
where (h, k) are the coordinates of the vertex.
Since the vertex is at (2,-1), h = 2 and k = -1.
Putting those values into the formula: y - -1 = a(x - 2)2 or y + 1 = a(x - 2)2
To find the value of a, substitute these values: y = 0 and x = 5 into the equation.
0 + 1 = a(5 - 2)2
1 = a(3)2
1 = 9a
a = 1/9
The equation is: y + 1 = (1/9)(x - 2)2
