Question

How do you write the equation of the quadratic that has the vertex of (2,-3) and a point on (0,1)?

Answer 1

`y=(x-2)^2-3`

Explanation:

Vertex form of a quadratic equation: `y=a(x-h)^2+k`, where (h, k) represents the vertex

Plug in (2, -3) for (h, k).

`y=a(x-2)^2+(-3)`

`y=a(x-2)^2-3 rarr` We still don't know what a is, so let's plug in the point (0, 1) to find what it is

`1=a(0-2)^2-3`

`1=a(-2)^2-3`

`1=a(4)-3`

`1=4a-3`

`4a=4`

`a=1`

Our equation would be `y=1(x-2)^2-3` once 1 is plugged in for a, but the 1 does not need to be written in the final answer because anything multiplied by 1 is itself

`y=(x-2)^2-3` is the equation in vertex form