SOLUTION: Identify the maximum or minimum (vertex), zeros, and axis of symmetry line and show the graph. {{{y=((1/2)x^2)-x-4}}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Identify the maximum or minimum (vertex), zeros, and axis of symmetry line and show the graph. {{{y=((1/2)x^2)-x-4}}}       Log On


   

Question 413891: Identify the maximum or minimum (vertex), zeros, and axis of symmetry line and show the graph.
y=%28%281%2F2%29x%5E2%29-x-4
Answer by bayners123(12) About Me  (Show Source):
You can put this solution on YOUR website!
maximum/minimum will be turning point. Differentiate the function y=%28%281%2F2%29x%5E2%29-x-4 which is what I think you mean gives you a gradient of x-1, so will have a minimum (minimum as is positive x%5E2 so a bowl shape with a minimum and no maximum) at x=1, at which point y = -4.5.
zeros;
x=0, y=-4 clearly
y=0, x%5E2+-2x+-8+=+0 - I multiplied by 2 to make easier
0=(x-4)(x+2), x= 4 or -2
Line of symmetry I am fairly sure it doesn't have as it is a function of x which is an odd function, and x^2 which is even.7
Drawing the graph should be fine now you know where it crosses the axes.