The coordinates of the vertex can be found by using the formula:
𝑣 = (−𝑏/2𝑎, 𝑓(−𝑏/2𝑎))
However, in the given equation, we do not have any value of 𝑏 as it is absent. Therefore, we cannot use the above formula to find the coordinates of the vertex.
However, we can still find the coordinates of the vertex using some other methods.
Method 1: Completing the Square
We can rewrite the given equation in vertex form by completing the square:
𝒚 = 𝒙^2
= 𝑥^2 + 0𝑥 + 0
= (𝑥 + 0)^2 - 0
Therefore, the equation in vertex form is: 𝒚 = (𝑥 + 0)^2 + 0
From this equation, we can see that the coordinates of the vertex are (0, 0).
Method 2: Visualize the Graph
The given equation represents a parabola that opens upwards (as the coefficient of 𝒙^2 is positive). Therefore, the vertex lies at the bottom of the parabola, which is the lowest point on the curve.
The graph of the given equation is:
y
^
|
| /\
| / \
| / \
| / \
| / \
|/__________\
-----------------------> x
We can see from the graph that the vertex is at the origin, which is (0, 0).
Therefore, the coordinates of the vertex are (0, 0).
The equation in vertex form 𝒚 = 𝒙^2 find the Coordinates of
vertex
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