Question

The graph of h is the graph of f(x) = x2 translated 2 units left and 5 units up. What is the vertex form of this function?

A. h(x) = (x + 2)2 + 5
B. h(x) = (x - 2)2 + 5
C. h(x) = (x + 5)2 + 2
D. h(x) = (x + 5)2 - 2

Answer 1

A.
`h(x) = (x+2)^(2)+5`

Explanation:

First, we need to defined the two transformations required to derive
`h(x)`.

Vertical translation

`n(x) = m(x) +k`,
`k \in \mathbb{R}` (1)

Where:

`k > 0`, upwards.

`k < 0`, downwards.

Horizontal translation

`n(x) = g(x+k)`,
`k\in \mathbb{R}` (2)

Where:

`k > 0`, leftwards.

`k < 0`, rightwards.

Let
`f(x) = x^(2)`, if
`h(x)` is translated 2 units left and 5 units up, then we have the resulting expression:

`h(x) = (x+2)^(2)+5` (3)

Hence, correct answer is A.