Identify the Graph of y = -x²: Matching Quadratic Functions

Q: How do I know which way a parabola opens?

Look at the coefficient of x²! If it's positive (like $ x^2 $), the parabola opens upward like a smile. If it's negative (like $ -x^2 $), it opens downward like a frown.

Q: Where is the vertex for y = -x²?

The vertex is at (0, 0) - the origin! Since there's no number added or subtracted from x², and no constant term, the parabola's lowest/highest point is right at the center of the coordinate plane.

Q: What's the difference between y = x² and y = -x²?

They're mirror images of each other! $ y = x^2 $ opens upward (U-shape), while $ y = -x^2 $ opens downward (upside-down U). Both have the same vertex at (0,0).

Q: How can I quickly identify the correct graph?

Use the two-step check:Does it open downward? (because of the negative sign)Is the vertex at (0,0)? (because there are no shifts)The graph that matches both criteria is your answer!

Q: What if I pick the wrong graph by accident?

You can always test a point! Try x = 1: $ y = -(1)^2 = -1 $. The correct graph should pass through (1, -1). If your chosen graph doesn't, pick a different one!

Quadratic Functions with Vertex Identification

One function

$y=-x^2$

for the corresponding chart

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Match the correct graph to the function

00:03 The coefficient of X squared is negative, meaning a sad parabola

00:08 We'll use the formula to describe a parabola

00:14 The term P equals (0), and the term K equals (0)

00:21 The X-axis intersection points according to the terms

00:27 We'll draw the function according to intersection points and parabola type

00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

One function

$y=-x^2$

for the corresponding chart

Step-by-step solution

To solve this problem, we should follow these steps:

Step 1: Understand the characteristics of the function $y = -x^2$ . This is a downward-opening parabola with its vertex at (0,0).
Step 2: Compare these characteristics against the provided graphs to find a match.
Step 3: Analyze each graph to identify the one that matches these characteristics. Specifically, a parabola that opens downwards with a vertex at the origin will be our match.

Let's go through these steps:
- The function $y = -x^2$ opens downward because of the negative coefficient and is centered at the origin. This gives the parabola a vertex at (0, 0).

Upon reviewing the provided graphs, option 2 corresponds to this function, as it depicts a downward-opening parabola with its vertex at the origin (0,0).

Therefore, the solution to the problem is choice 2.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Direction Rule: Negative coefficient makes parabola open downward
Vertex Location: For $y = -x^2$ , vertex is at origin (0,0)
Graph Check: Verify downward opening and vertex at (0,0) match ✓

Common Mistakes

Avoid these frequent errors

Confusing upward and downward opening parabolas
Don't assume all parabolas open upward = wrong graph selection! The negative sign in front of x² flips the parabola downward. Always check the coefficient sign: positive opens up, negative opens down.

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 know which way a parabola opens?

Look at the coefficient of x²! If it's positive (like $x^2$ ), the parabola opens upward like a smile. If it's negative (like $-x^2$ ), it opens downward like a frown.

Where is the vertex for y = -x²?

The vertex is at (0, 0) - the origin! Since there's no number added or subtracted from x², and no constant term, the parabola's lowest/highest point is right at the center of the coordinate plane.

What's the difference between y = x² and y = -x²?

They're mirror images of each other! $y = x^2$ opens upward (U-shape), while $y = -x^2$ opens downward (upside-down U). Both have the same vertex at (0,0).

How can I quickly identify the correct graph?

Use the two-step check:

Does it open downward? (because of the negative sign)
Is the vertex at (0,0)? (because there are no shifts)

The graph that matches both criteria is your answer!

What if I pick the wrong graph by accident?

You can always test a point! Try x = 1: $y = -(1)^2 = -1$ . The correct graph should pass through (1, -1). If your chosen graph doesn't, pick a different one!

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