The equation in vertex form 𝒚 = 𝒙^2 find the Coordinates of
vertex
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).
To find the coordinates of the vertex in the equation 𝑦 = 𝑥^2, we can rewrite it in the vertex form 𝑦 = 𝑎(𝑥 − ℎ)^2 + 𝑘, where (ℎ, 𝑘) represents the coordinates of the vertex.
Comparing the given equation 𝑦 = 𝑥^2 to the vertex form, we can see that 𝑎 = 1, ℎ = 0, and 𝑘 = 0.
Therefore, the coordinates of the vertex are (0, 0).