Answer:
y = (1/25)x^2 - 1
Explanation:
To begin, we can use the fact that the x-intercepts of the parabola are at (5, 0) and (-6, 0) to determine the x-intercepts form of the equation. The x-intercepts form of a parabola is given by:
(x - r)(x - s) = 0,
where r and s are the x-coordinates of the x-intercepts.
Using this form, we can write:
(x - 5)(x + 6) = 0
Expanding this equation gives:
x^2 + x - 30 = 0
Next, we use the fact that the vertex of the parabola is at (0, -1) to determine the y-intercept form of the equation. The y-intercept form of a parabola is given by:
y = a(x - h)^2 + k,
where (h, k) is the vertex.
Substituting (0, -1) into this equation gives:
y = a(x - 0)^2 - 1
Simplifying gives:
y = ax^2 - 1
Now we can use the fact that the parabola passes through the point (5, 30) to determine the value of a. Substituting x = 5 and y = 0 into the equation above gives:
0 = a(5)^2 - 1
Solving for a gives:
a = 1/25
Substituting this value of a into the equation above gives the final equation of the parabola:
y = (1/25)x^2 - 1