Final answer:
To find the quadratic function with x-intercepts (4,0) and (5,0) and y-intercept (0,4), we can use the fact that the x-intercepts occur when f(x) = 0, and the y-intercept occurs when x = 0. By solving the equations formed by substituting the coordinates, we find the quadratic function f(x) = 4.9x^2 - 14.3x + 4.
Step-by-step explanation:
A quadratic function is defined as f(x) = ax^2 + bx + c, where a, b, and c are constants. To find the quadratic function with x-intercepts (4,0) and (5,0) and y-intercept (0,4), we can use the fact that the x-intercepts occur when f(x) = 0, and the y-intercept occurs when x = 0.
Since the x-intercepts are (4,0) and (5,0), we can write the equations 4a + 4b + c = 0 and 5a + 5b + c = 0. Since the y-intercept is (0,4), we have c = 4.
By substituting c = 4 into the equations above, we can solve for a and b. The solution is a = 4.9 and b = -14.3. Therefore, the quadratic function is f(x) = 4.9x^2 - 14.3x + 4.