1)Use a system of equations to find the parabola of the form y=ax^2+bx+c that go
ID: 3082950 • Letter: 1
Question
1)Use a system of equations to find the parabola of the form y=ax^2+bx+c that goes through the three given points. (2,20),(-4,38),(-2,8) 2)FIND AN EQUATION THROUGH THE LINE THROUGH THE GIVEN POINTS (1,1)(-2,-5) 3)Two numbers have a sum of 47 their difference is 3. what are the two numbers? 4)An investment of $54,000 was made by a business club. The investment was split into three parts and lasted one year. The first part of the investment earned 8% interest, the second 6% and the third 9%. Total interest from the investments was $4260. The interest from the investment was 6 times the interest from the second. Find totals of the three parts of the investment. What is the amount of the first part of the investment?Explanation / Answer
You're given these three points (0, 0), (-4, 16), (-3, 6) And you have your equation y = ax² + bx + c Now let's plug in all the information 0 = a(0)² + b(0) + c c = 0 16 = a(-4)² + b(-4) + c 16= 16a - 4b + c 6 = a(-3)² + b(-3) + c 6 = 9a - 3b + c We have 3 equations and 3 variables, so, let's solve for all these variables. c = 0 16 = 16a - 4b + c 6 = 9a - 3b + c Here, we quickly know that c = 0, so we can now boil down 3 eqtn and 3 variables into 2 eqtns and 2 variables. 16 = 16a - 4b 6 = 9a - 3b a = 2, b = 4, c = 0 Now if we plug these points back into the quadratic form... y = ax² + bx + c y = 2x² + 4x + 0 y = 2x² + 4x Therefore, your equation is y = 2x² + 4x
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