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BELLWORK • Describe the relationship between the real solutions of 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 and the graph of 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐. QUADRATIC EQUATIONS REAL LIFE SITUATIONS BLOOD PRESSURE The graph illustrates that a person’s normal systolic blood pressure, measured in millimeters of mercury (mm Hg), depends on his or her age. (The graph starts at 100 mm Hg). The formula 𝑃 = 0.006𝐴2 − 0.02𝐴 + 120 Models a man’s normal systolic blood pressure P at age A. a.) find the age, to the nearest year, of a man whose normal systolic blood pressure is 125 mm Hg. b.) use the graph to describe the differences between the normal systolic blood pressure of men and women as they age. BLOOD PRESSURE • The formula 𝑃 = 0.01𝐴2 + 0.05𝐴 + 107 models a women's normal systolic blood pressure, P, at age A. Use this formula to find the age, to the nearest year, of a women whose normal systolic blood pressure is 115 mm Hg. Use the graph to verify your solution. THE PYTHAGOREAN THEOREM • The sum of the squares of the lengths of the legs of a right triangle equals the square of the length of the hypotenuse. If the legs have the length a and b, and the hypotenuse has length c, then 𝑎2 + 𝑏 2 = 𝑐 2 c a b USING THE PYTHAGOREAN THEOREM a.) A wheelchair ramp with the length of 122 inches has a horizontal distance of 120 inches. What is the ramps vertical distance. b.) Construction laws are very specific when it comes to access ramps for the disabled. Every vertical rise of 1 inch requires a horizontal run of 12 inches. Does this ramp satisfy the requirement. TELEVISION • In a 25-inch television set, the length of the screen’s diagonal is 25 inches. If the screen’s height is 15 inches, what is it’s width? DOES IT MAKE SENSE? Determine whether each statement makes sense or does not make sense, and explain your reasoning. 2 1) Because I want to solve 25 x 169 0 fairly quickly, I’ll use the quadratic equation. 2) I’m looking at a graph with one x-intercept, so it must be the graph of a linear equation? 3) I obtained -17 for the discriminant, so there are two imaginary solutions. 4) When I use the square root property to determine the length of a right triangles side, I don’t even bother to list the negative square root. TRUE/FALSE Determine if the statement is true or false. If it is false, make the necessary changes to make it true. 2 ( 2 x 3 ) 25 is equivalent to 2x 3 5 1) The equation 2) Any quadratic equation that can be solved by completing the square can be solved by the quadratic formula. 3) The quadratic formula is developed by applying factoring and the zero product principle to the quadratic equation ax 2 bx c 0 4) In using the quadratic formula to solve the quadratic equation 5 x 2 2 x 7 , we have a=5, b= 2, c= -7