Final answer:
The standard form equation of a parabola, we use the x-intercepts and a point on the graph. We substitute these values into the equation y = ax^2 + bx + c and solve for the coefficients a, b, and c. Once we have the values of a, b, and c, we can write the equation of the parabola in standard form.
Step-by-step explanation:
The standard form equation of a parabola is given by y = ax^2 + bx + c.
We are given that the parabola has x-intercepts of 3 and -1, which means that the parabola crosses the x-axis at these points. Hence, these points lie on the x-axis and will have a y-coordinate of 0. Substituting these values into the equation, we get two equations: 0 = a(3)^2 + b(3) + c and 0 = a(-1)^2 + b(-1) + c.
We are also given that the parabola passes through the point (-2, 10). Substituting these values into the equation, we get the third equation: 10 = a(-2)^2 + b(-2) + c.
Now we have three equations with three variables (a, b, and c) that can be solved simultaneously to find their values. Once we have the values of a, b, and c, we can substitute them back into the standard form equation to get the equation of the parabola.