1. **State the problem:** We are given two points on a parabola: the vertex at $(6,7)$ and another point $(4,13)$. The parabola is described by the vertex form equation: $$y = a(x - h)^2 + k$$ where $(h,k)$ is the vertex. 2. **Identify known values:** From the vertex, we have $h=6$ and $k=7$. The point $(4,13)$ lies on the parabola, so it must satisfy the equation. 3. **Substitute known values into the equation:** $$13 = a(4 - 6)^2 + 7$$ Simplify inside the parentheses: $$13 = a(-2)^2 + 7$$ $$13 = 4a + 7$$ 4. **Solve for $a$:** Subtract 7 from both sides: $$13 - 7 = 4a$$ $$6 = 4a$$ Divide both sides by 4: $$a = \frac{6}{4} = \frac{3}{2}$$ 5. **Write the final equation:** Substitute $a=\frac{3}{2}$, $h=6$, and $k=7$ back into the vertex form: $$y = \frac{3}{2}(x - 6)^2 + 7$$ This is the equation of the parabola. **Answer:** $$y = \frac{3}{2}(x - 6)^2 + 7$$