Linear Function y=(x+2)²: Graph Matching and Point Identification

Match the function

$y=(x+2)^2$

for the corresponding chart

To solve this problem, we'll determine which graph represents the line given by $y=(x+2)^2$.

• Step 1: The y-intercept for the function $y = x + 2$ is at point $(0, 2)$.

• Step 2: Another point can be found by substituting $x = -4$, giving $y = -4 + 2 = -2$, so point $(-4, -2)$.

• Step 3: Based on these points, we identify a slope of $\frac{2 - (-2)}{0 - (-4)} = 1$.

• Step 4: Check each graph to find the one that includes these details: y-intercept at 2 and another point at $(-4, -2)$.

Upon examining each option, we find that the graph matching these points and features corresponds to choice 3.

Thus, the correct graph is option 3.