Final answer:
The quadratic equation in vertex form with a vertex at (5, -2) and passing through the point (6, 1) is y = 3(x - 5)^2 - 2.
Step-by-step explanation:
The student needs to write the equation of a quadratic in vertex form that has a vertex at (5, -2) and passes through the point (6, 1). The vertex form of a quadratic equation is:
y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
To find the value of 'a', we use the given point (6, 1). Since the parabola passes through this point, we substitute x = 6 and y = 1 into the vertex form and solve for 'a':
1 = a(6 - 5)^2 + (-2)
1 = a(1)^2 - 2
3 = a.
Now that we have the value of 'a', we can write the equation:
y = 3(x - 5)^2 - 2.
This is the required quadratic equation in vertex form with the given vertex and point.