Final answer:
The standard equation of the parabola is y = 5(x - 1)² + 3.
Step-by-step explanation:
The standard equation of a parabola with a vertex (h, k) is given by the equation y = a(x - h)² + k, where (h, k) is the vertex of the parabola and a is a constant. To find the equation of a parabola with a vertex (1, 3) and containing the point (0, 8), we can substitute these values into the equation.
Substituting the vertex coordinates (h, k) = (1, 3) and the point coordinates (x, y) = (0, 8) into the standard equation, we have 8 = a(0 - 1)² + 3. Simplifying and solving for a, we find that a = 5.
Finally, substituting the value of a into the standard equation, we obtain the standard equation of the parabola y = 5(x - 1)² + 3.