Question

Find the Quadratice function
`y=a(x-h)x^(2)` with given vertex (5,8) and given point (1,3)

Answer 1

Given:

Consider the quadratic function is

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

With given vertex (5,8) and given point (1,3).

To find:

The equation of quadratic function.

Solution:

The quadratic function is

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

Where, (h,k) is the vertex and a is a constant.

Vertex is (5,8). So,

`(5,8)=(h,k)`

`h=5,k=8`

Putting
`h=5,k=8` in (i), we get

`y=a(x-5)^2+8` ...(ii)

The given point is (1,3). Putting x=1 and y=3 in (ii), we get

`3=a(1-5)^2+8`

`3-8=a(-4)^2`

`-5=16a`

`-(5)/(16)=a`

Putting
`a=-(5)/(16)` in (ii), we get

`y=-(5)/(16)(x-5)^2+8`

Therefore, the required quadratic function is
`y=-(5)/(16)(x-5)^2+8`.