find minimum or maximum valuevalue

Question

y=-3x (x-7)

Answer 1

y = -3x(x-7) = -3x² + 21x

 

This is a quadratic equation, so its graph is a parabola.  The vertex of the parabola will be the maximum or minimum point.  Let's put the quadratic into its vertex form, y = a(x-h)²+k, where (h,k) is the location of the vertex.  To convert to the vertex form, complete the square:

 

y = -3(x² - 7x + (-7/2)²) - 3*(7/2)²

 

y = -3(x - (7/2))² - 36.75

 

The vertex is located at the point (7/2,36.75). Since the coefficient of the x² term (3) is positive, this parabola opens downward with the vertex at the top.  The vertex is thus the maximum point and has a value of y = 36.75.