Question

The vertex of a quadratic function is located at (1, 4), and the y-intercept of the function is (0, 1). What is the value of a if the function is written in the form y = a(x – h)2 + k?

a =

Answer 1

-3

Explanation:

Answer 2

`\large\boxed{y=-3(x-1)^2+4}`

Explanation:

The vertex form of a quadratic function:

`y=a(x-h)^2+k`

where (h, k) is a vertex.

We have the vertex (1, 4). Therefore h = 1 and k = 4.

The y-intercept of the function is (0, 1). Put x = 0 and y = 1 to the equation

`y=a(x-1)^2+4`

`1=a(0-1)^2+4`

`1=a(-1)^2+4`

`1=1a+4` subtract 4 from both sides

`-3=a\to a=-3`