Comparing Vertices: When is x² Equal to 2x² at the Same Point?

The vertex of the function y=x2 y=x^2 is the same vertex of the function y=2x2 y=2x^2 .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Do the functions have the same vertex point?
00:06 We'll use the formula to calculate the vertex point of a parabola
00:12 Let's look at the function coefficients
00:15 We'll substitute in the formula and calculate the vertex point
00:23 We'll substitute the X value we found to find the vertex point
00:27 This is the vertex point of the first function
00:31 We'll use the same method to find the vertex point for the second function
00:52 We can see that the vertex points are equal
00:56 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

The vertex of the function y=x2 y=x^2 is the same vertex of the function y=2x2 y=2x^2 .

2

Step-by-step solution

The given functions are y=x2 y = x^2 and y=2x2 y = 2x^2 . Both functions are written in the form y=ax2 y = ax^2 , where the vertex for such parabolas is determined by setting x=0 x = 0 .

Let's analyze each function step-by-step:

  • Function y=x2 y = x^2 :
    This function represents a parabola that opens upwards with its vertex located at (0,0)(0, 0).
  • Function y=2x2 y = 2x^2 :
    Similarly, this function is also a parabola that opens upwards. The coefficient 22 affects the "narrowness" or "width" of the parabola but does not shift the vertex, so the vertex remains at (0,0)(0, 0).

Both functions y=x2 y = x^2 and y=2x2 y = 2x^2 share the same vertex at the point (0,0)(0, 0). Therefore, the statement that the vertex of the function y=x2 y=x^2 is the same vertex of the function y=2x2 y=2x^2 is True.

Thus, the correct answer to the problem is True.

3

Final Answer

True.

Practice Quiz

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Find the intersection of the function

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

With the X

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