To write the equation of the parabola in vertex form, we can use the formula y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. We are given that the vertex is (1, 1) and a point on the parabola is (2, -5). We can use this information to find the value of a and write the equation of the parabola in vertex form.
Step-by-step method:
Use the vertex coordinates to write the parabola's equation in the form y = a(x - h)^2 + k.
Find the value of the coefficient a by using the point (2, -5) on the parabola.
Substitute the values of h, k, and a into the equation to write the equation of the parabola in vertex form.
Using the given vertex (1, 1) and point (2, -5), we can find the value of a as follows:
y = a(x - h)^2 + k
-5 = a(2 - 1)^2 + 1
-5 = a(1)^2 + 1
-6 = a
Therefore, a = -6. Now we can substitute the values of h, k, and a into the equation to write the equation of the parabola in vertex form:
y = -6(x - 1)^2 + 1
In summary, the equation of the parabola in vertex form is y = -6(x - 1)^2 + 1, where the vertex is (1, 1) and a point on the parabola is (2, -5).