Vertex (1,3) point (2,5)

Answer 1

I am going to assume the question is to write the equation of a parabola in vertex form using the given point and vertex. We will be filling in the general formula: y = a(x-h)^2 + k

h = x value of the vertex

k = y value of the vertex

a = stretch or shrink factor

Once we get numbers for h,k, and a, we have our equation.

We are given the vertex (1,3) and a point (2,5). It looks like we have h and k —> h=1 and k=3.

We are missing a, so we are going to use the extra point to help us solve for a in the general formula. The extra point will fill in the spots for x and y temporarily to help us get a.

This is the information we will plug in for the general formula:

x=2

y=5

h=1

k=3

a=?

5 = a(2-1)^2 + 3

solve for a using PEMDAS

parentheses (2-1) = 1 and then exponent 1^2 = 1

5 = a*1 + 3 subtract 3

2 = a*1

a =2

Now we have a=2, h=1, k=3 and we can plug them into the general formula to get the final equation:

y = 2(x-1)^2 + 3

If this was not the intended question please let me know! Thanks

Answer 2

Hello Mike,

I assume you are looking to get the vertex form equation of the parabola that passes through those 2 points.

You probably know the vertex form formula to use: y = a*(x-h)² + k; where (h,k) are the vertex coordinates

First: plug the vertex coordinates: y = a*(x- 1)² + 3

Next, plug the other point (aka, replace x and y in the equation by the x and y coordinates of the point you're given): 5 = a*(2- 1)² + 3

5 = a*(1)² + 3

5 = a + 3

a = 2

So the equation is: y = 2*(x- 1)² + 3