Question

Write a formula for quadratic function if its graph has the vertex at point (−2,5) and passes through the point (3,−10).

Answer 1

Basically it's the expanded version of the person who already answered. It's -3/5(x)^2-12/5 x+ 13/5

Answer 2

The formula for the quadratic function is
`y=5 - (3)/(5) \left(x + 2\right)^(2)`.

Explanation:

The quadratic function with vertex
`(h,k)` is given by
`y=a \left(- h + x\right)^(2) + k`.

We know that the vertex is
`(-2,5)`. Thus, the formula for the quadratic function is

`y=a \left(x + 2\right)^(2) + 5`

To find
`a`, use the fact that the quadratic function passes through the point
`\left(3, -10\right)` and we solve for
`a`.

`-10=a \left(3 + 2\right)^(2) + 5\\a\left(3+2\right)^2+5=-10\\5^2a+5=-10\\25a+5=-10\\25a=-15\\(25a)/(25)=(-15)/(25)\\a=-(3)/(5)`

Thus, the formula for the quadratic function is
`y=5 - (3)/(5) \left(x + 2\right)^(2)`.