1. **State the problem:** We need to find the equation of a parabola in vertex form that passes through points $(-4,3)$ and $(2,3)$ and has a maximum value of 10. 2. **Recall the vertex form of a parabola:** $$y = a(x - h)^2 + k$$ where $(h,k)$ is the vertex. Since the parabola has a maximum value 10, the vertex is at $(h,k) = (-1,10)$ (given approximately). 3. **Use the vertex to write the equation:** $$y = a(x + 1)^2 + 10$$ 4. **Use a point to find $a$:** The parabola passes through $(-4,3)$. Substitute $x = -4$, $y = 3$: $$3 = a(-4 + 1)^2 + 10$$ $$3 = a(-3)^2 + 10$$ $$3 = 9a + 10$$ $$9a = 3 - 10 = -7$$ $$a = -\frac{7}{9}$$ 5. **Write the final equation:** $$y = -\frac{7}{9}(x + 1)^2 + 10$$ 6. **Domain and range:** - Domain: All real numbers, since a parabola extends infinitely left and right. $$\text{Domain}: (-\infty, \infty)$$ - Range: Since the parabola opens downward (negative $a$) and has maximum $y=10$, $$\text{Range}: (-\infty, 10]$$