MATH : Review for Chapter Can ou use the Zero-Product Propert to solve quadratic equations b factoring? () Solve each equation b factoring. 6 7 8 + = + ( ) = 8 7p ( p ) p ( p) = = c = c = + Can ou solve a quadratic equation b etracting square roots? () Solve each quadratic equation b etracting square roots. Leave our solutions with no square-root smbols in the denominator. = 7 7 0 = 7 ( + ) = 8 ( ) Can ou solve a quadratic equation b completing the square? () Solve each quadratic equation b completing the square. = 8 0 = + = ( ) 7 + = ( 9 + 7) = ( + 9) Can ou solve a quadratic equation using the Quadratic Formula? () Use the Quadratic Formula to solve each quadratic equation. = = 0 ( ) ( + 7) + 8 = = 6 Can ou use the discriminant to determine whether a quadratic equation has two unequal real solutions, a repeated real solution, or no real solution, without solving the equation? Can ou verif our results with a graphing utilit? () Determine the number of real solutions for each quadratic equation, and verif our results using a graphing utilit. 8 0 + = = 6 + = 0 7 + + = 0
Can ou solve equations that are quadratic in form? (6) Solve each equation. Find the real solutions. 7 = 6 b + 7 = 8b + 8 = 9 6 + = + = 0 (f) + 7 = 0 (g) ( + ) ( + ) = 0 [Hint: Let u = +.] (h) + + + 6 = 0 [Hint: Let u = +.] Can ou identif the ke features of the graph of a quadratic function without using a graphing utilit? (7) For each quadratic function, identif the (i) verte; (ii) -intercepts; (iii) -intercept; (iv) maimum or minimum value; and (v) ais of smmetr. Sketch the graph without using a graphing utilit. f = + + g = f = + g = + 9 f = ( + ) (f) g = + 8 Can ou solve a maimizing or minimizing application problem? (8) Solve each problem. The manufacturer of a CD plaer has found that the revenue R (in dollars) is given b R = p + 700p, when the unit price is p dollars. If the manufacturer sets the price p to maimize revenue, what is the maimum revenue to the nearest dollar? The owner of a video store has determined that profits P (in dollars) of the store are approimatel given b P = + 60 + 60, where is the number of videos rented dail. Find the maimum profit to the nearest dollar. The owner of a video store has determined that the cost C (in dollars) of operating the store is approimatel given b C = 8 + 70, where is the number of videos rented dail. Find the lowest cost to the nearest dollar.
A projectile is fired from a cliff 00 feet above the water at an inclination of o to the horizontal, with a muzzle speed of 0 feet per second. The height h of the projectile above the water is given b h = + + 00, where is the horizontal distance of the ( 0) projectile from the base of the cliff. Find the maimum height of the projectile. (9) Solve each problem. John has 00 feet of fencing available. He wishes to enclose rectangular area. (i) Epress the area of the rectangle as a function of its length, l. (ii) What is the domain of the area function? (iii) What are the dimensions of the rectangle that produce the largest area? What are the dimensions of the largest rectangle that can be enclosed with 6 feet of fencing? A developer wants to enclose a rectangular grass lot that borders a cit street for parking. If the developer has feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed? Can ou solve a problem using the Quadratic Regression feature of a graphing utilit? (0) Solve each application problem using a graphing utilit. Southern Granite and Marble sells granite and marble b the square ard. One of its granite patterns is price sensitive. If the price is too low, customers perceive that it has less qualit. If the price is too high, customers perceive that it is overpriced. The compan conducted a pricing test with potential customers. The following data was collected. Use a graphing calculator to plot the data. What is the quadratic function of best fit? Price Buers b $0 0 0 0 0 6 60 7 80 7 00 0 0
An engineer collects data showing the speed S of a given car model and its average miles per gallon M. Use a graphing calculator to plot the scatter diagram. What is the quadratic function of best fit? Speed S mpg M 0 8 0 0 0 0 60 8 70 80 The number of housing starts in one beachside communit remained fairl level until 99 and then began to increase. The following data shows the number of housing starts since 99 ( = ). Use a graphing calculator to plot a scatter diagram. What is the quadratic function of best fit? Year Housing starts h 00 0 0 0 6 0 7 0 8 0 Can ou perform arithmetic operations on comple numbers and epress our results in standard form? () Perform the operations and epress our results in the form a + bi. i + ( i) ( i) + i i ( i) ( i) + + + i i (f) ( + i) ( i) (g) ( i) ( + i) Can ou solve quadratic equations in the comple number sstem? () Solve each equation. + 9 = 0 + 9 = 0 + 6 = 0 + + = 0
Answers: () = or = = or = 9 p = 0 or p = = or = 7 9 c = or c = (f) = or = () = ± = ± 6 = or = = ± 7 () = ± 0 = ± ± = = 9 or = 8 () ± = 6 = or = 7 ± 9 = = ± () two unequal real solutions a repeated real solution two unequal real solutions no real solution (6) = ± or = ± b = ± or b = ± = or = = or = 7 = 6 (f) = or = (g) = or = (h) =, =, =, or = 6
(7) (i) (, ) (ii) 0. and. (iii) (iv) (v) = (i) (iv), (ii) (v) and (iii) = (i) (, ) (ii) none (iii) 9 (iv) (v) = (i),0 (ii) (iv) 0 (v) = (iii) 9 (i) (, ) (ii).6 and 6. (iii) (iv) (v) = (f) (i), 0 (ii) (iii) 8 (iv) 0 (v) = (8) $80,6 $960 $6 approimatel 7.0 feet (9) (i) Area = A ( l) = l ( 0 l) (ii) Domain: { l : 0 l 0} (iii) Dimensions are feet b feet feet b feet,79 ft (0) b + 0.0.. M S S + S + 0.006 0.70. h + +.679 6.607 68.7
() i + i i i i i + i i = = = = = + i + i i i i + i i = i + 8i i = + i = + i 8 + i + i i i i i i i i = = = = = i + + i i i i (f) + 6i (g) () + 9 = 0 = 9 = ± 9 = ± i using the Quadratic Formula, ( ) ± 9 ± ± 6 + i = = = = ( ± i) = = ± i = ± 6i ± 7i 7 = = ± i