Final answer:
To find the standard equation of a parabola with a vertical axis, you need to identify the vertex and the x-intercepts. Then, you can use these values to determine the value of a and write the equation in the standard form.
Step-by-step explanation:
The standard equation of a parabola with a vertical axis can be written as: y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
Given that the x-intercepts are -1 and 13, we know that the parabola intersects the x-axis at x = -1 and x = 13. This means that the factors of the equation will be (x + 1) and (x - 13).
Also, since the highest point has a y-coordinate of 7, the vertex of the parabola will be (h, 7). Substituting these values into the equation, we can solve for the value of a and determine the standard equation of the parabola.