To write the equation of the parabola in vertex form, we can use the general vertex form of a quadratic equation:

$y = a(x - h)^2 + k$

Where:

• $(h, k)$ is the vertex of the parabola.
• $a$ is a coefficient that determines the direction and width of the parabola.

From the graph:

• The vertex is $(0, 180)$, so $h = 0$ and $k = 180$.
• Another point on the graph is $(1, 164)$, which we can substitute into the equation to solve for $a$.

Starting with the equation: $y = a(x - 0)^2 + 180 \quad \text{or} \quad y = ax^2 + 180$

Now, substitute $(x, y) = (1, 164)$: $164 = a(1)^2 + 180$ $164 = a + 180$ $a = 164 - 180 = -16$

Thus, the equation of the parabola in vertex form is: $y = -16x^2 + 180$

Would you like more details on this process or have any questions?

Here are five related questions:

1. How would the equation change if the vertex was different?
2. Can you convert this vertex form into standard form?
3. How do you determine if a parabola opens upward or downward?
4. What is the role of the coefficient $a$ in transforming the shape of the parabola?
5. How can you find the x-intercepts from this vertex form?

Tip: When finding the equation of a parabola, always make sure you correctly identify the vertex and use another point to solve for the constant $a$.