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

Question

One function

y=−(x+2)2 y=-(x+2)^2

for the corresponding chart

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

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
00:14 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 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.

Answer

3

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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