Question

Find the vertex of the parabola: y = x^2. Simplify both coordinates and write them as proper fractions, improper fractions, or integers.

Answer 1

The equation of the parabola is given by \( y = x^2 \).

This is a standard form of a parabola that opens upwards. The vertex of a parabola in the form \( y = ax^2 + bx + c \) can be found using the formula for the vertex \( x \)-coordinate:
\[
x = -\frac{b}{2a}
\]
In this case, the coefficients are:
- \( a = 1 \)
- \( b = 0 \)
- \( c = 0 \)

Substituting the values of \( a \) and \( b \):
\[
x = -\frac{0}{2 \cdot 1} = 0
\]

Next, we substitute \( x = 0 \) back into the equation to find the \( y \)-coordinate of the vertex:
\[
y = (0)^2 = 0
\]

Thus, the vertex of the parabola \( y = x^2 \) is:
\[
(0, 0)
\]

In proper fraction, improper fraction, or integers, the coordinates of the vertex can be expressed as:
\[
\left(0, 0\right)
\]