Final answer:
The equation of the parabola with vertex at (-2, 3) that passes through (0, 8) is y = (5/4)(x + 2)^2 + 3.
Step-by-step explanation:
The equation of a parabola can be written in the standard form y = ax^2 + bx + c, where a, b, and c are coefficients and the vertex form is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
To find the specific equation of the parabola with a vertex at (-2, 3) that passes through the point (0, 8), we first use the vertex form. The general equation becomes y = a(x + 2)^2 + 3, since the vertex (h, k) is (-2, 3). We can determine the value of a by substituting the point (0, 8) into the equation: 8 = a(0 + 2)^2 + 3. Simplifying this, we get 5 = 4a, therefore a = 5/4.
The final equation of the parabola is y = (5/4)(x + 2)^2 + 3.