Question

What is the equation of a parabola that is a vertical translation of `y=-5x^2+4x-3` of -12 and a horizontal translation of -9?

Answer 1

`y=-5(x+9)^2+4(x+9)-15`
`y=−5x^2−86x−384`

Explanation:

To ma(x+e this easier, let's call our function `f(x)`

To vertically translate the function by `a` we just add `a`, `f(x)+a`.

To horizontally translate a function by `b`, we do `x-b`, `f(x-b)`

The function needs to be translated 12 units down and 9 units to the left, so we will do:
`f(x+9)-12`

This gives us:
`y=-5(x+9)^2+4(x+9)-3-12`

`y=-5(x+9)^2+4(x+9)-15`

After expanding all the brackets, multiplying by factors and simplifying, we get:
`y=−5x^2−86x−384`