ASSIGNMENT 13DYLAN ZWICK’S MATH 1010 CLASS1. Section 8.3In Exercises 1-4, write the quadratic equation in general form.8.3.1: 2x2= 7 − 2x8.3.2: 7x2+ 15x = 58.3.4: x(2x + 9) = 12In Exercises 5-14, solve the equation first by using the quadratic f or-mula and then by fa ctoring. See Examples 1-4.8.3.5: x2− 11x + 28 = 08.3.7: x2+ 6x + 8 = 08.3.8: x2+ 9x + 14 = 08.3.9: 16x2+ 8x + 1 = 012 DYLAN ZWICK’S MATH 1010 CLASSIn Exercises 15-40, solve the equation by using the quadratic for-mula. (Find all real and complex solutions)8.3.15: x2− 2x − 4 = 08.3.18: y2+ 6y − 8 = 08.3.21: 2x2+ 3x + 3 = 08.3.25: 2x2+ 4x − 3 = 08.3.27: −4x2− 6x + 3 = 08.3.30: 6x2+ 3x − 9 = 08.3.35: 2x − 3x2= 3 − 7x2ASSIGNMENT 13 3In Exercises 41, 49, use the discriminant to determine the type ofsolution(s) of the quadratic equation. See Example 5.8.3.41: x2+ x + 1 = 08.3.45: 9x2− 24x + 16 = 0In Exercises 49, 55, solve the quadratic equation by using the mostconvenient method. (Find all real and complex solutions.)8.3.49: z2− 169 = 08.3.55: 2y(y − 18) + 3(y − 18) = 0In Exercises 65, 69, write a quadratic equation having the given so-lutions. See Example 6.8.3.65: 5, −28.3.69: 1 +√2, 1 −√2In Exercises 89, 92, solve the equation.8.3.89:x24−2x3= 14 DYLAN ZWICK’S MATH 1010 CLASS8.3.92:√2x − 3 = x − 28.3.100: The path of a baseball after it has been hit is given byh = −0.003x2+ 1.19x + 5.2where h is the height ( in feet) of the baseball and x is thehorizontal distance (in feet) of the ball from home plate. Theball hits the top of the outfield fence that is 10 feet high. Howfar is the outfield fence from home plate?ASSIGNMENT 13 52. Section 8.4In Exercises 1-6, match the equation with its graph.6 DYLAN ZWICK’S MATH 1010 CLASSASSIGNMENT 13 78 DYLAN ZWICK’S MATH 1010 CLASS8.4.1: y = (x + 1)2− 38.4.2: y = −(x + 1)28.4.3: y = x2− 38.4.4: y = −x2− 38.4.5: y = (x − 2)28.4.6: y = 2 − (x − 2)2In Exercises 7- 18, write the equation of the parabola in standardform and find the vertex of its graph. See Example 1.8.4.7: y = x2− 2x8.4.9: y = x2− 4x + 7ASSIGNMENT 13 98.4.12: y = x2− 4x + 58.4.15: y = −x2− 8x + 5In Exercises 19 , 22, find the vertex of the gra ph of the function byusing the formula x = −b2a. See example 2.8.4.19: f(x) = x2− 8x + 158.4.22: h(x) = −x2+ 14x − 14In Exercises 25-34, state whether the graph opens upward or down-ward, and find the vertex.8.4.25: y = 2(x − 0)2+ 28.4.28: y = 2(x − 12)2+ 38.4.30: y = −(x + 1)2In Exercises 35-46, find the x- and y-intercepts of the graph.8.4.35: y = 25 − x28.4.39: y = −x2− 6x + 78.4.44: y = x2− 3x − 10In Exercises 47-70, sketch the parabola. Identify the vertex and anyx-intercepts. Use a graphing calculator to verify your results.8.4.47: g(x) = x2− 410 DYLAN ZWICK’S MATH 1010 CLASS8.4.51: f(x) = x2− 3x8.4.69: f(x) = 5 −13x2In Exercises 7 1, 74, identify t he transformation of the graph off(x) = x2, and sketch a graph of h.8.4.71: h(x) = x2− 18.4.74: h(x) = (x − 4)28.4.100: Path of a Sortball. The height y (in feet) of a softballthat yo u hit is given byy = −170x2+ 2x + 2where x is the ho rizontal distance (in feet) from where youhit the ball.(a) How high is t he ball when you hit it?ASSIGNMENT 13 11(b) How high is the ball at its maximum height?(c) How far from where you hit the ball does it strike theground?12 DYLAN ZWICK’S MATH 1010 CLASS3. Section 8.58.5.1: A store owner bo ught a case of eggs fo r $21.60. By the timeall but 6 dozen of the eggs had been sold at a profit of $0.30per dozen, the original investment of $21.60 had been regained.How many dozen eggs did the owner sell , and what was theselling price per dozen?8.5.3: A flea market vendor buys a box of DVD movies for $50.After selling several of the DVDs at a profit of $3 each, thevendor still has 15 of the DVDs left by the time she regains her$50 investment. How many DVDs has the vendor sold, and atwhat price?8.5.4: A sorority buys a case of sweatshirts for $ 750 to sell at amixer. The sorority needs to sell all but 20 of the sweatshirtsat a profit of $10 per sweatshirt to regain the $750 investment.How many sweatshirts must be sold, and at what price, to dothis?ASSIGNMENT 13 13In Exercises 5, 11, complete the table of widths, lengths, perimeters,and areas of rectangles.8.5.5, 11:Width Length Perimeter Area1.4l l 54in.w w + 3 54km8.5.15: A picture frame is 4 inches taller than it is wide and hasan area of 192 square inches. What are the dimensions of thepicture frame?8.5.20: You have 100 feet of f encing. Do you have enough to en-close a rectangular region whose area is 630 square feet? Is thereenough to enclose a circular area of 630 square feet? Explain.In Exercises 23, 25 find the interest rate r. Use the formular A =P (1 + r)2, where A is the amount after 2 years in an account earning rpercent (in decimal form) comp ounded annually , and P is the originalinvestment.8.5.23: P = $10, 000, A = $11, 990.258.5.25: P = $500, A = $572.4514 DYLAN ZWICK’S MATH 1010 CLASS8.5.29: A service organization pays $210 for a block of tickets toa baseball game. The block contains three more tickets thanthe organization needs f or its members. By inviting three morepeople to attend (and share in the cost), the organization lowersthe price per person by $3.50. How many p eople are going tothe game?8.5.31: Delivery Rate. You deliver pizzas to an insurance officeand an apartment complex (see figure). Your total mileagein derving to the insurance office and then to t he apartmentcomplex is 12 miles. By using a direct route, yo u are able todrive just 9 miles to teturn to the pizza shop. Estimate thedistance from the pizza shop to the insurance office.ASSIGNMENT 13 158.5.35: An office conta ins two printers. Machine B is known totake 3 minutes longer than machine A to produce the com-pany’s monthly financial report. Using both machines together,it t akes 6 minutes to produce the report. How long would ittake each machine to produce the report ?8.5.41: The height h in feet of a baseball t seconds aft er being hitat a point 3 feet above the ground is given by h = 3+75t−16t2.Find the time when the ball hits the ground.8.5.49: Find two consecutive odd integers such that their productis 323.16 DYLAN ZWICK’S MATH 1010 CLASS4. Section 8.6In Exercises 1-10, find the critical numbers.8.6.1: x(2x − 5)8.6.2: 5x(x − 3)8.6.6: y(y − 4) − 3(y − 4)8.6.10: 4x2− 4x − 3In Exercises 11-20, determine the intervals