Question - Solving for 'a' and 'b' in a Quadratic Equation Passing Through Two Points
Solution:
The question in the image provides an equation of a graph, y = ax^2 + bx, and mentions that this graph passes through two points: (1,1) and (3,2). To find the values of 'a' and 'b', we can substitute these points into the equation to form a system of linear equations, which we can then solve to find the values of 'a' and 'b'.Let's substitute point (1,1):1 = a(1)^2 + b(1)1 = a + b ... (1)Now, we substitute point (3,2):2 = a(3)^2 + b(3)2 = 9a + 3b ... (2)We now have a system of two equations with two variables. Equation (1) can be rewritten as b = 1 - a.Let's substitute b from equation (1) into equation (2):2 = 9a + 3(1 - a)2 = 9a + 3 - 3a2 = 6a + 3Now we solve for 'a':6a = 2 - 36a = -1a = -1/6With 'a' found, we can now find 'b' by substituting 'a' back into equation (1):1 = (-1/6) + bb = 1 + 1/6b = 6/6 + 1/6b = 7/6Therefore, the values of 'a' and 'b' are:a = -1/6b = 7/6
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