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

Quadratic Functions with Vertex Form Graphs

One function

y=−(x−5)2 y=-(x-5)^2

for the corresponding chart

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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 written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

One function

y=−(x−5)2 y=-(x-5)^2

for the corresponding chart

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

2

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.

3

Final Answer

1

Key Points to Remember

Essential concepts to master this topic
  • Form Analysis: y=−(x−5)2 y = -(x-5)^2 shows vertex at (5,0) and opens downward
  • Technique: Negative coefficient means parabola opens down, vertex h-value is 5
  • Check: At x = 5: y=−(5−5)2=0 y = -(5-5)^2 = 0 , confirming vertex (5,0) ✓

Common Mistakes

Avoid these frequent errors
  • Confusing the direction the parabola opens
    Don't think y=−(x−5)2 y = -(x-5)^2 opens upward = wrong graph selection! The negative sign in front means the parabola is flipped and opens downward. Always check the coefficient of the squared term first.

Practice Quiz

Test your knowledge with interactive questions

Find the intersection of the function

\( y=(x-2)^2 \)

With the X

FAQ

Everything you need to know about this question

How do I find the vertex from y=−(x−5)2 y = -(x-5)^2 ?

+

In vertex form y=a(x−h)2+k y = a(x-h)^2 + k , the vertex is at (h, k). Here, h = 5 and k = 0, so the vertex is (5, 0).

Why does the negative sign make it open downward?

+

The coefficient of the squared term determines direction. When it's negative (like -1 here), the parabola flips upside down and opens downward instead of upward.

What if I see y=−(x+5)2 y = -(x+5)^2 instead?

+

Be careful with signs! y=−(x+5)2 y = -(x+5)^2 means y=−(x−(−5))2 y = -(x-(-5))^2 , so the vertex would be at (-5, 0), not (5, 0).

How can I tell which graph shows a vertex at (5, 0)?

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Look for the graph where the parabola's highest point (since it opens down) is directly above x = 5 on the horizontal axis and touches y = 0.

Do I need to plot other points to identify the graph?

+

Not usually! The vertex location and opening direction are typically enough to identify the correct graph from multiple choices.

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