Final answer:
To find the equation of the parabola in vertex form with a given vertex and point, we use the vertex form equation y = a(x - h)^2 + k and solve for 'a'.
Step-by-step explanation:
To find the equation of the parabola in vertex form, we can use the vertex form equation: y = a(x - h)^2 + k. In this equation, (h, k) represents the vertex of the parabola. Given that the vertex is (3, 4), we can substitute these values into the equation: y = a(x - 3)^2 + 4. Now, we need to find the value of 'a'.
Next, we need to use the fact that the point (-1, -4) lies on the parabola. Substituting these values into the equation, we have: -4 = a(-1 - 3)^2 + 4. Solving this equation will give us the value of 'a'.
Once we have the value of 'a', we can substitute it back into the equation y = a(x - 3)^2 + 4 to get the equation of the parabola in vertex form.