Final answer:
The question relates to a quadratic function, which can be solved using the quadratic formula to find the roots. The function in question is f(x)=-2x²+20x-53, and the quadratic formula is applied using coefficients a, b, and c from the equation.
Step-by-step explanation:
The student's question involves a quadratic function, which is a mathematical expression of the form f(x) = ax² + bx + c. In this case, the provided equation is f(x)=-2x²+20x-53. To solve for the roots of this quadratic equation or to find the x-intercepts of the function's graph, one can employ the quadratic formula, which is x = (-b ± √(b² - 4ac))/(2a). The constants a, b, and c in this formula would correspond to the coefficients in the provided equation, where a = -2, b = 20, and c = -53.
As an example, solving an equation of the form ax² + bx + c = 0 using given constants a = 4.90, b = 14.3, and c = -20.0 would involve plugging these values into the quadratic formula to find the solutions for x.