Question

6.
axis of symmetry: $x = 1$
vertex: $(1, 2)$
write an equation for the graphed function.
$y = $

Explanation:

Step1: Identify function type

The graph is V-shaped, so it's an absolute value function. The vertex form is $y = a|x - h| + k$, where $(h,k)$ is the vertex.

Step2: Plug in vertex values

Given vertex $(1,2)$, substitute $h=1$, $k=2$: $y = a|x - 1| + 2$.

Step3: Find 'a' using a point

Pick a point on the graph, e.g., left side: when $x=-7$, $y=6$ (estimated from grid). Substitute:
$6 = a|-7 - 1| + 2$ → $6 = 8a + 2$ → $8a = 4$ → $a = \frac{1}{2}$.

Answer:

$y = \frac{1}{2}|x - 1| + 2$