Final answer:
To determine the equation of the parabola with zeros 5 and 9 and passing through the point (11, 24), we use the factored form and the given point to solve for the coefficient a, then expand to find the parabola in standard form.
Step-by-step explanation:
The student is asking to determine the equation of a parabola in standard form given the zeros (5 and 9) and a point on the parabola ((11, 24)). Since the zeros of the parabola are given, we can formulate the factored form of the quadratic equation as f(x) = a(x - 5)(x - 9). To find the value of a, we can use the given point by substituting x and y with 11 and 24, respectively, and solve for a. Once we have the value of a, we expand the equation to get the parabola in standard form, which is ax² + bx + c.
Using the point (11, 24), we get the equation 24 = a(11 - 5)(11 - 9). Solving for a, we find that a = 24 / ((11 - 5)(11 - 9)) = 24 / (6 × 2) = 2. The expanded standard form of the parabola is then f(x) = 2(x - 5)(x - 9) = 2x² - 28x + 90.