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

00:06 Let's find which graph matches the function.
00:10 The X squared term is negative, so the parabola is facing down, like a sad face.
00:17 Term P is five. Remember that.
00:21 Term K is zero. Got it?
00:24 Look at the X-axis intersection points. They're based on our terms.
00:29 Now, let's draw the graph using those points and our down-facing parabola.
00:39 And that's how we find the right graph. Great job!

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