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15. Consider the quadratic with equation y = ax + bx + c that passes through the points (1, 22), (6, 7 ) and (5, - 2). 15a First set up a system of equations in the variables a, b and c using the points given. The first equation has been written for you: Equation 1: atbtc 22 Equation 2: 7 36 a + 6 b+c Equation 3: -2 25 a+ 5 b+c 15b Next subtract Equation 3 from both Equation 1 and Equation 2 to form two new equations that involve only a and b: Equation 1: atbtc 22 subtract Equation 3: 25a + 5b + c -2 to give Equation 4: = 24 -24 a + (-4) b and Equation 2: 36a + 6b + c = 7 subtract Equation 3: 25a + 56 + c -2 to give Equation 5: 9 11 at 1 6 15c Next rearrange Equation 5 to make b the subject: b=9 - 1la15. Consider the quadratic with equation y = ax + bx + c that passes through the points (1, 22), (6, 7 ) and (5, - 2). b =9 - 1la 150 Next substitute this result into Equation 4 to obtain an equation just in terms of a, and then solve for a. X = a=9- 1la V 0 = 3 15e Substitute the value of a that you just obtained into the rearranged form of Equation 5 to obtain b: v b= -24 15f Now substitute your values of a and b into one of the first three equations and solve for c. C = 43 15g Finally, write down the quadratic equation that passes through the points (1, 22), (6, 7 ) and (5, - 2). Enter your next step here ()