Question

The equation in vertex form 𝒚 = 𝒙^2 find the Coordinates of
vertex

Answer 1

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).