Did you know?
Did you know that for a parabola in the form y = a(x-h)^2 + k, the vertex is located at the point (h, k)? In the given equation, y = 5(x - 1)^2 - 10, the vertex is therefore located at (1, -10).
Furthermore, did you know that for a parabola in the form y = a(x-h)^2 + k, the focus is located at the point (h, k + 1/(4a))? In this parabola, the focus is given by (1, -10 + 1/20), which simplifies to (1, -9.95).
Lastly, did you know that for a parabola in the form y = a(x-h)^2 + k, the directrix is a horizontal line given by the equation y = k - 1/(4a)? In this case, the directrix would be y = -10 - 1/20, or more simply y = -10.05.
By understanding these properties, it becomes easier to visualize and analyze parabolas.
