To write the equation of a parabola in vertex form, the general formula is:

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

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

Given:

• Vertex: $(-3, 8)$, which gives $h = -3$ and $k = 8$,
• Y-intercept: $(0, -1)$, which helps us find $a$.

Step 1: Plug the vertex into the equation

$y = a(x + 3)^2 + 8$

Step 2: Use the y-intercept $(0, -1)$ to find $a$

Substitute $x = 0$ and $y = -1$ into the equation: $-1 = a(0 + 3)^2 + 8$ $-1 = a(9) + 8$ $-1 - 8 = 9a$ $-9 = 9a$ $a = -1$

Step 3: Write the final vertex form equation

Now that we know $a = -1$, the equation becomes: $y = -(x + 3)^2 + 8$

Thus, the vertex form of the equation is: $y = -(x + 3)^2 + 8$

Would you like more details on the solution? Here are 5 related questions to consider:

1. How do you convert a vertex form equation to standard form?
2. What does the value of $a$ tell us about the parabola's shape and direction?
3. How can you find the axis of symmetry from the vertex form equation?
4. How do you determine the x-intercepts (if any) from this equation?
5. Can you describe how the vertex form helps in graphing a parabola more easily?

Tip: In vertex form, the sign of $a$ tells you whether the parabola opens upward ($a > 0$) or downward ($a < 0$).