Homework Sourse1 gx 3x2 30x 76 Express the quadratic function in standar
1. g(x) = 3x^2 - 30x + 76
Express the quadratic function in standard form. ________
Find its maximum or minimum value. ( The answer is NOT positive/negative 5 ) _________
2. f(x) = - x^2 + 6x
Express the quadratic function in standard form. ________
Solution
1. g(x) = 3x2 - 30x + 76 Then g(x) = 3(x2 - 10x + 25) + 1 = 3( x - 5)2 + 1. This is the equation of a parabola which opens upwards. The vertex of the parabola is ( 5, 0). Since the parabola opens upwards, its vertex is the lowest point. Hence g(x) is minimum when x = 5.
Alternatively, let y = g(x) = 3x2 - 30x + 76 . Then dy/dx = 6x - 30. We have a minimum when dy/dx = 0 i.e. when 6x -30 = 0 or when x = 5.
2. f(x ) = - x2 + 6x = -( x2 - 6x + 9) + 9 = - (x-3)2 + 9
