Question

What is the vertex of the parabola y=
1
3
x2–5?

Answer 1

The equation of the parabola you provided is in the form \( y = ax^2 + bx + c \), where:

- \( a = \frac{1}{3} \)
- \( b = 0 \) (since there is no \( x \) term)
- \( c = -5 \)

To find the vertex of the parabola, we can use the formula for the x-coordinate of the vertex, which is given by:

\[
x = -\frac{b}{2a}
\]

Substituting the values of \( a \) and \( b \):

\[
x = -\frac{0}{2 \cdot \frac{1}{3}} = 0
\]

Now, we can find the y-coordinate of the vertex by substituting \( x = 0 \) back into the equation:

\[
y = \frac{1}{3}(0)^2 - 5 = -5
\]

Therefore, the vertex of the parabola is at the point:

\[
(0, -5)
\]