I can help you with that! To find the equation of the parabola given the vertex at (2,-11) and passing through the point (0,5), you can follow these steps:
1. The general equation of a parabola in vertex form is: y = a(x - h)^2 + k, where (h,k) is the vertex.
2. Substitute the vertex coordinates into the equation: y = a(x - 2)^2 - 11.
3. Use the point (0,5) to find the value of 'a':
Substitute (0,5) into the equation: 5 = a(0 - 2)^2 - 11.
Solve for 'a': 5 = 4a - 11.
4a = 16.
a = 4.
4. Substitute 'a' back into the equation: y = 4(x - 2)^2 - 11.
Therefore, the equation of the parabola with the given vertex and passing through the point is:
y = 4(x - 2)^2 - 11.
