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

Answer:

A. $h(x) = (x+2)^{2}+5$

Step-by-step 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.