Vertex Form 1Cf261

1. **State the problem:** We need to find the equation of a parabola in vertex form given the vertex $(-3, 3)$ and a point on the parabola $(-4, 0)$. 2. **Recall the vertex form of a parabola:** $$y = a(x - h)^2 + k$$ where $(h, k)$ is the vertex. Here, $h = -3$ and $k = 3$, so the equation becomes: $$y = a(x + 3)^2 + 3$$ 3. **Use the given point $(-4, 0)$ to find $a$:** Substitute $x = -4$ and $y = 0$ into the equation: $$0 = a(-4 + 3)^2 + 3$$ $$0 = a(-1)^2 + 3$$ $$0 = a(1) + 3$$ $$0 = a + 3$$ 4. **Solve for $a$:** $$a = -3$$ 5. **Write the final equation:** $$y = -3(x + 3)^2 + 3$$ This is the equation of the parabola in vertex form with vertex $(-3, 3)$ and passing through $(-4, 0)$, opening downward because $a$ is negative.