Question

What is the equation of the parabola that has a vertex at `(-18, 2)` and passes through point `(-3,-7)`?

Answer 1

In vertex form we have:

`y=-1/25(x+18)^2+2`

Explanation:

We can use the vertex standardised form:

`y=a(x+d)^2+k`

As the vertex `->(x,y)=(color(green)(-18),color(red)(2))`

Then `(-1)xxd=color(green)(-18)" "=>" "d=+18`

Also `k=color(red)(2)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So now we have:

`y=a(x+d)^2+k" "->" "y=a(x+18)^2+2`

Using the given point of `(-3,-7)` we substitute to determine `a`

`y=a(x+18)^2+2" "->" "-7=a(-3+18)^2+2`

`" "-7=225a+2`

`" "(-7-2)/225=a`

`" "a=-1/25`

Thus `y=a(x+d)^2+k" "->" "y=-1/25(x+18)^2+2`