Final answer:
The maximum temperature reached can be found by identifying the vertex of the parabola represented by the quadratic function. The time of day when this occurs is determined by the axis of symmetry formula, and the maximum temperature is calculated by substituting that time into the original function.
Step-by-step explanation:
To find the maximum temperature reached on a particular summer day as modeled by the function f(t) = -t2 + 5.3t + 87, where t is the number of hours after noon, we need to identify the vertex of the parabola represented by the quadratic function. Since the parabola opens downward (the coefficient of t2 is negative), the vertex will be the highest point on the graph, representing the maximum temperature.
To find the time of day when the maximum temperature occurs, we calculate the axis of symmetry using the formula t = -b/(2a). Here, a = -1 and b = 5.3. Substituting these values, we get t = -5.3 / (2 * -1) = 2.65 hours after noon, which is around 2:39 p.m.
Substituting t = 2.65 into the original function to find the maximum temperature, we get f(2.65) = -(2.65)2 + (5.3 * 2.65) + 87. After calculations, we determine the maximum temperature to be the result of this calculation.