Question

How to identify a vertical and horizontal translation
of a quadratic function.

Answer 1

Answer & Step-by-step explanation:

The equation that is often used for translations of quadratics is the vertex form:

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

This is for a parabola (the graph of a quadratic is a U-ish, V-ish curve called a parabola) that opens up or down. If you have a number inside the parenthesis with the x, such as (x+2) or (x-7) then the parabola will translate or slide left or right. If you alter the x, the curve gets moved in the x-direction left or right. This is the trickier translation bc its a bit backwards from what you expect. (x - 2) moves the curve 2 units to the RIGHT. (x + 7) moves the curve 7 units LEFT.

Then the vertical translations are the number tacked on the end in the vertex form of the equation. + 4 means translate(slide) the curve up 4 units. Whereas, a -3 at the end of the equation would slide the curve down 3 units.

So, for example

y = (x + 1)^2 + 5

The parabola would slide LEFT 1 and UP 5.

Answer 2

Identify h and k of
`y=a(x-h)^2+k`

Explanation:

Hi there!

First, we would have to organize the quadratic function in vertex form:

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

a = vertical stretch

h = horizontal translation

k = vertical translation

If h is positive, the function moves to the right. If it is negative, the function moves to the left.

If k is positive, the function moves up. If it is negative, the function moves down.

I hope this helps!