Match the Graph: Identifying y=x² Among Four Parabola Options

Q: How can I tell which way a parabola opens?

Look at the coefficient of $ x^2 $! If it's positive (like +1 in $ y = x^2 $), the parabola opens upward. If it's negative, it opens downward.

Q: Where should the vertex of y = x² be located?

The vertex of $ y = x^2 $ is always at the origin (0,0). This is the lowest point of the parabola since it opens upward.

Q: What points should I check to verify the correct graph?

Test easy points like (1,1) and (-1,1). When x = 1, y = 1² = 1. When x = -1, y = (-1)² = 1. The parabola should pass through both points.

Q: Why are some parabolas in different positions?

Parabolas can be shifted up, down, left, or right from the basic $ y = x^2 $ shape. But for $ y = x^2 $ specifically, it must be centered at the origin with no shifts.

Q: What if two graphs look similar?

Check the vertex location first, then test a few points. Only one graph will have its vertex at (0,0) AND pass through points like (2,4) and (-2,4).

Parabola Recognition with Vertex Position

To which chart does the function $y=x^2$ correspond?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find the right function using our data.

00:08 We're focusing on the positive side of the graph, which means our parabola opens upwards.

00:14 This indicates a positive coefficient for X squared.

00:18 To represent a parabola, we'll use a special formula.

00:22 Here, the terms P and K both equal zero.

00:28 Let's substitute these values into the formula to find our function.

00:37 We'll then sketch the function based on intersection points and the parabola's shape.

00:43 And that's how we solve this problem!

Step-by-step written solution

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Understand the problem

To which chart does the function $y=x^2$ correspond?

Step-by-step solution

To solve this problem, let's go through the process of elimination to find the graph corresponding to $y = x^2$ .

The function $y = x^2$ is an upward-opening parabola with its vertex located at the origin point (0, 0). It is symmetric about the y-axis.

Based on our problem statements or diagrams, the given function will match with chart '2'. This chart will depict an upward-facing parabolic shape with no horizontal or vertical shifts.

Therefore, the solution to the problem is the chart labeled 2.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Standard Form: $y = x^2$ opens upward with vertex at origin (0,0)
Identification: Look for U-shaped curve passing through points like (1,1) and (-1,1)
Verification: Check that curve is symmetric about y-axis and passes through (0,0) ✓

Common Mistakes

Avoid these frequent errors

Confusing upward and downward opening parabolas
Don't choose a downward-opening parabola for $y = x^2$ = negative coefficient mistake! A positive coefficient means the parabola opens upward like a smile. Always remember: positive $x^2$ coefficient means upward opening.

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 can I tell which way a parabola opens?

Look at the coefficient of $x^2$ ! If it's positive (like +1 in $y = x^2$ ), the parabola opens upward. If it's negative, it opens downward.

Where should the vertex of y = x² be located?

The vertex of $y = x^2$ is always at the origin (0,0). This is the lowest point of the parabola since it opens upward.

What points should I check to verify the correct graph?

Test easy points like (1,1) and (-1,1). When x = 1, y = 1² = 1. When x = -1, y = (-1)² = 1. The parabola should pass through both points.

Why are some parabolas in different positions?

Parabolas can be shifted up, down, left, or right from the basic $y = x^2$ shape. But for $y = x^2$ specifically, it must be centered at the origin with no shifts.

What if two graphs look similar?

Check the vertex location first, then test a few points. Only one graph will have its vertex at (0,0) AND pass through points like (2,4) and (-2,4).

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