An expression is shown below f(x)=2x^2-3x-5 part a: what are the x intercepts of the graph of f(x)? show your work. part b: is the vertex of the graph f(x) going to be a minimum or maximum? what are the coordinates of the vertex? justify your answers and show your work. part c: what are the steps you would use to graph f(x)? justify that you can use the answers obtained in part a and b to draw the graph

Find the horiz. intercepts of  f(x)=2x^2-3x-5.  to do this, set  f(x)=2x^2-3x-5 = 0 and solve for x.  i chose to use synthetic div. to check out roots and lucked out on the first try:   one root is x=5/2.  then the other root has to be -1.check:   does (2x-5)(x+1) give us  f(x)=2x^2-3x-5?                         2x^2 + 2x   - 5?   yes, this is correct.the x-intercepts are x=5/2 and x=-1, or (-1,0) and (5/2,0).min or max?   because the coefficient (2) of the x^2 term is positive, the graph opens up, meaning that we'll have a minimum.let's find the coordinates of the vertex by completing the square: 2x^2 + 2x    - 5  can be rewritten as 2(x^2 + x                    ) - 5                                            or as      2(x^2 + x + 1/4 - 1/4)    -5, or as:                                                           2(x^2 + x + 1/4) - 1/2 - 5                                            or          2(x+1/2)^2 - 11/2the coordinates of the vertex are x = -1/2 and y = -11/2:   (-1/2, -11/2).