Final answer:
To write an equation of a parabola with given intercepts and a point, we can create a system of equations and solve for the coefficients of the quadratic equation. The equation of the parabola is y = -11.25x^2 + 14.8x + 3.
Step-by-step explanation:
To write an equation of a parabola with x-intercepts at (1/4,0) and (-3,0) which passes through the point (0,3), we can start by using the fact that the x-intercepts are given. These x-intercepts are the points where the graph of the parabola intersects the x-axis, meaning that the y-coordinate is 0. The x-intercepts are (1/4,0) and (-3,0), which gives us the equations (1/4)^2a + (1/4)b + c = 0 and (-3)^2a + (-3)b + c = 0. We can also use the point (0,3) to find another equation: 0^2a + 0b + c = 3.
Now we have a system of three equations with three unknowns (a, b, and c) which we can solve to find the equation of the parabola. Solving this system of equations, we find that the equation of the parabola is y = -11.25x^2 + 14.8x + 3.