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

Quadratic Functions with Vertex Form Transformations

One function

y=−(x+2)2 y=-(x+2)^2

for the corresponding chart

222-2-2-2222-2-2-21234

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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 coefficient of X squared is negative, meaning a sad parabola
00:14 The term P equals (-2)
00:27 The term K equals (0)
00:31 The intersection points with X-axis according to the terms
00:37 Let's draw the function according to intersection points and parabola type
00:48 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

One function

y=−(x+2)2 y=-(x+2)^2

for the corresponding chart

222-2-2-2222-2-2-21234

2

Step-by-step solution

The function y=−(x+2)2 y = -(x+2)^2 represents a downward-opening parabola with the vertex at (−2,0)(-2, 0). This transformation involves a horizontal shift to the left by 2 units from the origin.

  • The vertex form of a quadratic function is y=a(x−h)2+k y = a(x-h)^2 + k , where (h,k)(h, k) represents the vertex.
  • In our function, h=−2 h = -2 and k=0 k = 0 , so the vertex is (−2,0)(-2, 0).
  • The coefficient of −1-1 indicates that the parabola opens downward.
  • Since the vertex (−2,0)(-2, 0) and the downward opening are correctly depicted in graph 3, this aligns with our function.

Therefore, after comparing the characteristics of the function with the given graphs, the corresponding graph for this function is option 3.

3

Final Answer

3

Key Points to Remember

Essential concepts to master this topic
  • Vertex Form: y=a(x−h)2+k y = a(x-h)^2 + k where vertex is (h,k)(h,k)
  • Technique: For y=−(x+2)2 y=-(x+2)^2 , vertex is (−2,0)(-2,0) and opens downward
  • Check: Negative coefficient means parabola opens downward, vertex at (−2,0)(-2,0) ✓

Common Mistakes

Avoid these frequent errors
  • Confusing the sign of the horizontal shift
    Don't think (x+2) (x+2) means shift right 2 units = vertex at (2,0)(2,0)! The plus sign actually means shift LEFT 2 units because we need x=−2 x = -2 to make the expression zero. Always remember (x−h) (x-h) means the vertex x-coordinate is h.

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 from y=−(x+2)2 y=-(x+2)^2 ?

+

Compare to vertex form y=a(x−h)2+k y = a(x-h)^2 + k . Here a = -1, h = -2, and k = 0. So the vertex is (−2,0)(-2, 0).

Why does the parabola open downward?

+

The coefficient a = -1 is negative! When a is negative, the parabola opens downward like an upside-down U. When a is positive, it opens upward.

What does the +2 inside the parentheses mean?

+

(x+2) (x+2) means the parabola shifts LEFT 2 units from the origin. Remember: (x+h) (x+h) shifts left, (x−h) (x-h) shifts right!

How can I tell which graph matches without calculating points?

+

Look for these key features:

  • Vertex location: Should be at (−2,0)(-2, 0)
  • Direction: Opens downward (negative coefficient)
  • Shape: Standard parabola width (coefficient is -1)

What if I need to find other points on the parabola?

+

Substitute x-values into y=−(x+2)2 y=-(x+2)^2 . For example: when x = -1, y=−(−1+2)2=−(1)2=−1 y = -(-1+2)^2 = -(1)^2 = -1 . The point (−1,−1)(-1, -1) is on the parabola!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Parabola Families questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations

Parabola of the Form y=(x-p)²

Calculate Area Under (x-3)²: Quadratic Function Analysis
Click to solve
Calculate Ascending Area of y=-(x+3)² : Quadratic Function Analysis
Click to solve