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

Question

One function

y=−(x−4)2 y=-(x-4)^2

for the corresponding chart

444-4-4-4-2-2-24441234

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
00:07 The term P equals (4)
00:12 The term K equals (0)
00:15 X-axis intersection points according to the terms
00:23 Let's draw the function according to the intersection points and parabola type
00:30 And this is the solution to the question

Step-by-Step Solution

The problem involves matching a given function y=−(x−4)2 y = -(x-4)^2 with its corresponding graph from multiple choices.

First, let's analyze the function:

  • The function is in vertex form y=a(x−h)2+k y = a(x-h)^2 + k , where the vertex is (h,k)(h, k).
  • Here, a=−1 a = -1 , h=4 h = 4 , and k=0 k = 0 , so the vertex is (4,0) (4, 0) .
  • The negative sign indicates the parabola opens downward.

To match the function with the correct graph:

  • Identify that the vertex of the parabola is at (4,0) (4, 0) .
  • The parabola is symmetric around the line x=4 x = 4 , opening downwards.

Upon examining the choices, Option 1 clearly shows a parabola with a vertex at (4,0) (4, 0) opening downward. This matches perfectly with the function y=−(x−4)2 y = -(x-4)^2 .

Therefore, the correct answer to the problem is 1.

Answer

1

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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