# What is the equation of the parabola that has a vertex at # (3, -3) # and passes through point # (0, 6) #?

##### 1 Answer

#### Explanation:

let's take the equation of the parabola as

two points are given as

just by looking at the two points, we can tell where the parabola intercepts the

from this, we can deduce that

now we only have to find the

since the vertex is

*this is a tip which is useful to remember.
- if the co-efficient of #x^2# is positive then the parabola has a minimum value.
- if the co-efficient of #x^2# is negative then the parabola has a maximum value.*

back to our problem,

since the vertex is

so the symmetrical point of (0,6) on the parabola would be (6,6)

so now we have three points altogether. i'm going to substitute these points to the equation we took and then i just have to solve the simultaneous equations i get.

substituting point (3,-3)

substituting point (6,6)

so the equation is

make the equation look more nicer,

graph{x^2-9x+18 [-10, 10, -5, 5]}