Match the Quadratic Function y=-(x-5)² to Its Correct Graph

Question

One function

y=−(x−5)2 y=-(x-5)^2

for the corresponding chart

555-5-5-5555-5-5-51234

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
00:09 Term P equals (5)
00:12 Term K equals (0)
00:16 X-axis intersection points according to the terms
00:23 Let's draw the function according to intersection points and parabola type
00:33 And this is the solution to the question

Step-by-Step Solution

We need to match the function y=−(x−5)2 y = -(x-5)^2 to the correct graph.

  • The graph will be a parabola that opens downward because of the negative sign in front.
  • The vertex of this parabola is (5,0)(5, 0) due to the function y=−(x−5)2 y = -(x-5)^2 .

Let’s analyze the characteristics of the graph:

  • The parabola is concave down (opens downward) since the square term is negative.
  • The vertex point of our equation must be located at (5,0)(5, 0).
  • This point indicates that the graph's highest point is at x=5 x = 5 .

Reviewing the options given in the chart, Option 1 correctly shows the vertex of the parabola at point (5,0)(5, 0), and it opens downward, as expected from a negative quadratic function.

The graph in accordance with the given function is option 1.

Answer

1

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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