5 – 1 Graphing Quadratic Functions Day 2 Objective: Use quadratic functions to solve real – life problems.

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5 – 1 Graphing Quadratic Functions Day 2 Objective: Use quadratic functions to solve real – life problems.

Example 5 Researchers conducted an experiment to determine temperatures at which people feel comfortable. The percent y of test subjects who felt comfortable at temperature x (in degrees Fahrenheit) can be modeled by: What temperature made the greatest percent of test subjects comfortable? At that temperature, what percent felt comfortable?

Solution: Since the leading coefficient is negative the parabola opens downward. The function has a maximum at its vertex. The temperature that the most test subjects felt comfortable occurred at 72 degrees.

At that temperature, what percent felt comfortable? To find the corresponding value of y (or output value of the function) substitute 72 for all x values in the original equation and compute At 72 degrees 92% of the test subjects were comfortable

Example 6: The Golden Gate Bridge in San Francisco has two towers that rise 500 feet above the roadway and are connected by suspension cables. Each cable forms a parabola with the equation. Where x and y are measured in feet. a) What is the distance d between the two towers? b) What is the height l above the road of the cable at its lowest point?

Solution a) The vertex is (2100, 8). The distance from one tower to the vertex is 2100 feet because the function is a quadratic we know that the graph is a parabola. The vertex lies on the axis of symmetry and both towers lie on the graph of the parabola they must be equal distance from the vertex. Therefore the distance between the towers must be 2 x 2100 ft or 4200 ft.

b) The lowest point the cable comes to the roadway is at the vertex and is the y portion of the vertex. Therefore the lowest the cable will come to the roadway is 8 ft.