Question

How do you write the standard form of the equation of the parabola that has a vertex at (8,-7) and passes through the point (3,6)?

Answer 1

`y=13/25*(x-8)^2-7`

Explanation:

The standard form of a parabola is defined as:

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

where `(h,k)` is the vertex

Substitute the value of the vertex so we have:

`y=a*(x-8)^2 -7`

Given that the parabola passes through point `(3,6)` ,so the coordinates of this point verifies the equation, let's substitute these coordinates by `x=3` and `y=6`

`6= a*(3-8)^2-7`
`6 = a*(-5)^2 -7`
`6 = 25*a -7`
`6+7 = 25*a`
`13 =25*a`
`13/25 = a`

Having the value of `a=13/25` and vertex`(8,-7)`

The standard form is:

`y=13/25*(x-8)^2-7`