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

Match the function

$y=(x+2)^2$

for the corresponding chart

Video Solution

Solution Steps

00:00 Match the correct graph to the function

00:03 The term P equals (-2)

00:11 The term K equals (0)

00:16 X-axis intersection points according to the terms

00:19 We'll use the square of sum formulas to open the parentheses

00:25 The coefficient of X squared is positive, meaning a smiling parabola

00:33 Let's draw the function according to the intersection points and parabola type

00:40 And this is the solution to the question

Step-by-Step Solution

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.