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

Q: How do I find the vertex of $ y=(x+2)^2 $ ?

In vertex form $ y=(x-h)^2+k $, the vertex is at (h, k). Since $ y=(x+2)^2 $ = $ y=(x-(-2))^2+0 $, the vertex is at (-2, 0).

Q: Why does the parabola open upward?

The coefficient of the squared term is positive (+1). When this coefficient is positive, the parabola opens upward like a smile. If it were negative, it would open downward.

Q: How do I find other points on the graph?

Pick any x-value and substitute! For example: when x = 0, $ y=(0+2)^2=4 $, giving point (0, 4). Try x = -1: $ y=(-1+2)^2=1 $, giving point (-1, 1).

Q: What's the difference between this and $ y=x^2 $ ?

The function $ y=(x+2)^2 $ is $ y=x^2 $ shifted 2 units left. The +2 inside the parentheses moves the parabola horizontally in the opposite direction.

Q: How can I tell which graph is correct?

Look for these key features: vertex at (-2, 0), passes through (0, 4), and opens upward. The parabola should be symmetric about the line x = -2.

Quadratic Functions with Graph Matching

Match the function

$y=(x+2)^2$

for the corresponding chart

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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 written solution

Follow each step carefully to understand the complete solution

Understand the problem

Match the function

$y=(x+2)^2$

for the corresponding chart

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.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Vertex Form: $y=(x+2)^2$ has vertex at (-2, 0)
Technique: Find key points like (0, 4) and (-4, 4) by substitution
Check: Verify parabola opens upward with vertex at (-2, 0) ✓

Common Mistakes

Avoid these frequent errors

Confusing the function with a linear equation
Don't treat $y=(x+2)^2$ as $y=x+2$ = straight line! This creates completely wrong points and graph shape. Always recognize the squared term means it's a parabola, not a line.

Practice Quiz

Test your knowledge with interactive questions

Find the intersection of the function

$$ y=(x-2)^2 $$

With the X

FAQ

Everything you need to know about this question

How do I find the vertex of $y=(x+2)^2$ ?

In vertex form $y=(x-h)^2+k$ , the vertex is at (h, k). Since $y=(x+2)^2$ = $y=(x-(-2))^2+0$ , the vertex is at (-2, 0).

Why does the parabola open upward?

The coefficient of the squared term is positive (+1). When this coefficient is positive, the parabola opens upward like a smile. If it were negative, it would open downward.

How do I find other points on the graph?

Pick any x-value and substitute! For example: when x = 0, $y=(0+2)^2=4$ , giving point (0, 4). Try x = -1: $y=(-1+2)^2=1$ , giving point (-1, 1).

What's the difference between this and $y=x^2$ ?

The function $y=(x+2)^2$ is $y=x^2$ shifted 2 units left. The +2 inside the parentheses moves the parabola horizontally in the opposite direction.

How can I tell which graph is correct?

Look for these key features: vertex at (-2, 0), passes through (0, 4), and opens upward. The parabola should be symmetric about the line x = -2.

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

Quadratic Functions with Graph Matching

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I find the vertex of $y=(x+2)^2$ ?

Why does the parabola open upward?

How do I find other points on the graph?

What's the difference between this and $y=x^2$ ?

How can I tell which graph is correct?

🌟 Unlock Your Math Potential

More Questions

Parabola of the Form y=(x-p)²

Match the Function y=-(x+2)² to its Corresponding Graph

Calculate Area Under (x-3)²: Quadratic Function Analysis

Match the Quadratic Function y=-(x-4)² to Its Graph: Visual Analysis

Identify the Graph of y = -x²: Matching Quadratic Functions

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

Quadratic Functions with Graph Matching

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I find the vertex of y=(x+2)2 y=(x+2)^2 y=(x+2)2?

Why does the parabola open upward?

How do I find other points on the graph?

What's the difference between this and y=x2 y=x^2 y=x2?

How can I tell which graph is correct?

🌟 Unlock Your Math Potential

More Questions

Parabola of the Form y=(x-p)²

Match the Function y=-(x+2)² to its Corresponding Graph

Calculate Area Under (x-3)²: Quadratic Function Analysis

Match the Quadratic Function y=-(x-4)² to Its Graph: Visual Analysis

Identify the Graph of y = -x²: Matching Quadratic Functions

How do I find the vertex of $y=(x+2)^2$ ?

What's the difference between this and $y=x^2$ ?