Final answer:
To write the equation of a quadratic function that passes through (4,3) and has x-intercepts of -1 and 5, we can use a system of equations to determine the values of a, b, and c.
Step-by-step explanation:
To write the equation of a quadratic function that passes through (4,3) and has x-intercepts of -1 and 5, we can use the form ax^2 + bx + c. Firstly, we know that the quadratic passes through the point (4,3), so when x = 4, y = 3. Substituting these values into the equation gives us the equation 16a + 4b + c = 3. Secondly, we can determine the equation using the x-intercepts. When x = -1 or x = 5, the quadratic is equal to 0. So, substituting these values into the equation gives us two more equations: a(-1)^2 + b(-1) + c = 0 and a(5)^2 + b(5) + c = 0. Solving this system of three equations will give us the values of a, b, and c, and thus the equation of the quadratic function.