Section 1.5 Ã¢Â€Â“ Solve Quadratic Equations - McGraw-Hill Ryerson

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$Math and Chemistry - McGraw-Hill Ryerson$

8. Determine the value(s) of k for which thequadratic equation x 2 kx 9 5 0 willhavea) two equal real rootsb) two distinct real roots9. a) Create a table ofvalues for thefunctionf (x) 5 2x 2 3xfor the domain{2, 1, 0, 1, 2, 3, 4}.b) Graph this quadratic function.c) On the same set of axes, graph the liney 5 6.d) Use your graph to determine theapproximate x-values where the liney 5 6 intersects the quadratic function.e) Determine the x-values for the points ofintersection of f (x) 5 2x 2 3x and thehorizontal line y 5 6 algebraically.10. Use Technology Check your answer toquestion 9 using a graphing calculator.11. What value(s) of k, where k is an integer,will allow each quadratic equation to besolved by factoring?a) x 2 kx 12 5 0RepresentingConnectingReasoning and ProvingProblem SolvingCommunicatingb) x 2 kx 5 8 c) x 2 3x 5 kSelecting ToolsReflecting12. The height, h, in metres, above the groundof a football t seconds after it is thrown canbe modelled by the functionh(t) 5 4.9t 2 19.6t 2. Determine howlong the football will be in the air, to thenearest tenth of a second.13. A car travelling at v kilometres per hourwill need a stopping distance, d, in metres,without skidding that can be modelledby the function d 5 0.0067v 2 0.15v.Determine the speed at which a car canbe travelling to be able to stop in eachdistance. Round answers to the nearesttenth of a metre.a) 37 m b) 75 m c) 100 m14. A by-law restricts the height of structuresin an area close to an airport. To conformwith this by-law, fuel storage tanks withdifferent capacities are built by varying theradius of the cylindrical tanks. The surfacearea, A, in square metres, of a tank withradius r, in metres, can be approximatelymodelled by the quadratic functionA(r) 5 6.28r 2 47.7r. What is the radius ofa tank with each surface area?a) 1105 m 2b) 896.75 m 215. The length of a rectangle is 2 m more thanthe width. If the area of the rectangle is20 m 2 , what are the dimensions of therectangle, to the nearest tenth of a metre?16. A building measuring 90 m by 60 m is tobe built. A paved area of uniform widthwill surround the building. The paved areais to have an area of 9000 m 2 . How wide isthe paved area?paved area17. If the same length is cut off three pieces ofwood measuring 21 cm, 42 cm, and 45 cm,the three pieces of wood can be assembledinto a right triangle. What length needs tobe cut off each piece?18. In Vancouver, the height, h, in kilometres,that you would need to climb to see to theeast coast of Canada can be modelled bythe equation h 2 12 740h 5 20 000 000.If the positive root of this equation is thesolution, find the height, to the nearestkilometre.50 MHR • Functions 11 • Chapter 1
19. Chapter Problem Andrea has been askedto determine when (if ever) the volume,V, in hundreds of shares, of a company’sstock, which can be modelled by thefunction V(x) 5 250x 5x 2 , after beinglisted on the stock exchange for x weeks,will reacha) 275 000 shares in a weekb) 400 000 shares in a weekWhat answer should Andrea give?20. Small changesto a quadraticRepresentingequation can havelarge effects on theConnectingsolutions. Illustratethis statement bysolving each quadratic equation.a) x 2 50x 624 5 0b) x 2 50x 625 5 0c) x 2 50x 626 5 0Achievement CheckReasoning and ProvingProblem SolvingCommunicatingSelecting ToolsReflecting21. A diver followed a path defined byh(t) 5 4.9t 2 3t 10 in her dive, wheret is the time, in seconds, and h representsher height above the water, in metres.a) At what height did the diver start herdive?b) For how long was the diver in the air?c) The 4.9 in front of the t 2 term isconstant because it relates to theacceleration due to gravity on Earth. Ifthe diver always starts her dives fromthe same height, what other value in thequadratic expression will never change?d) What is the only value in the quadraticexpression that can change? Suggest away in which this value can change.e) If the value in part d) changed to 6, howmuch longer would the diver be in theair?C Extend22. Complete the square on the expressionax 2 bx c 5 0 to show how thequadratic formula is obtained.23. A cubic block of concrete shrinks as itdries. The volume of the dried block is30.3 cm 3 less than the original volume,while the length of each edge hasdecreased by 0.1 cm. Determine the edgelength and volume of the concrete blockbefore it dried.24. In the diagram, the square has side lengthsof 6 m. The square is divided into three righttriangles and one isosceles triangle. Theareas of the three right triangles are equal.a) Find the value of x.b) Find the area of the acute isoscelestriangle.x6 m6 m25. Math Contest If f (x) 5 2x 2 13x c andf (c)5 16, then one possible value for c isA 2 B 2 C 4 D 826. Math Contest The functionf (x) 5 3x 2 9x 3 has x-interceptsp and q. The value of p pq q is___A 2B 3 5 13 C 0xD 427. Math Contest The squares MNOP andIJKL overlap as shown. K is the centre ofMNOP. What is the area of quadrilateralKROQ in terms of the area of MNOP?MPKQNOJRLI1.5 Solve Quadratic Equations • MHR 51
Page 2 and 3: Example 1Select a Strategy to Solve
Page 4 and 5: ) The parabola opens upward and the
Page 6 and 7: Since the discriminant is greater t

Section 1.5 Ã¢Â€Â“ Solve Quadratic Equations - McGraw-Hill Ryerson

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