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

Question

One function

y=−x2 y=-x^2

for the corresponding chart

-1-1-11234

Video Solution

Solution Steps

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 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.

Answer

2

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Related Subjects

Family of Parabolas y=(x-p)² Families of Parabolas

Question Types

Parabola of the Form y=(x-p)²: Match functions to the appropriate graphs