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

One function

y=−x2 y=-x^2

for the corresponding chart

-1-1-11234

❤️ 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
00:08 We'll use the formula to describe a parabola
00:14 The term P equals (0), and the term K equals (0)
00:21 The X-axis intersection points according to the terms
00:27 We'll draw the function according to intersection points and parabola type
00:34 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=−x2 y=-x^2

for the corresponding chart

-1-1-11234

2

Step-by-step solution

To solve this problem, we should follow these steps:

  • Step 1: Understand the characteristics of the function y=−x2 y = -x^2 . This is a downward-opening parabola with its vertex at (0,0).
  • Step 2: Compare these characteristics against the provided graphs to find a match.
  • Step 3: Analyze each graph to identify the one that matches these characteristics. Specifically, a parabola that opens downwards with a vertex at the origin will be our match.

Let's go through these steps:
- The function y=−x2 y = -x^2 opens downward because of the negative coefficient and is centered at the origin. This gives the parabola a vertex at (0, 0).

Upon reviewing the provided graphs, option 2 corresponds to this function, as it depicts a downward-opening parabola with its vertex at the origin (0,0).

Therefore, the solution to the problem is choice 2.

3

Final Answer

2

Practice Quiz

Test your knowledge with interactive questions

Find the intersection of the function

\( y=(x+4)^2 \)

With the Y

🌟 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

Match the Quadratic Function y=-(x-4)² to Its Graph: Visual Analysis
Click to solve
Linear Function y=(x+2)²: Graph Matching and Point Identification
Click to solve