Find a function whose graph is a parabola with vertex (4, 3) and that passes through the point (−3, 2).

Question

Find a function whose graph is a parabola with vertex (4, 3) and that passes through the point (−3, 2).

Answer 1

The general equation of a parabola is y = a(x – h)² + k where (h, k) denotes the vertex.

Your problem states that the vertex is (4, 3), so let's plug that into our equation:

y = a(x – 4)² + 3

Now we need to find what a is. Let's plug in the given point of (-3, 2):

2 = a(-3 – 4)² + 3

2 = a(-7)² + 3

2 = 49a + 3

-1 = 49a

a = -1/49

Now we can plug a into our equation to get our final equation:

y = (-1/49)(x-4)² + 3