SOLUTION: Without drawing the given ewuation, determine A)how many x-intercepts the parabola has B)whether its vertex lies above or on below or on the x-axis. Show your work. y=-x^2-5x

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: Without drawing the given ewuation, determine A)how many x-intercepts the parabola has B)whether its vertex lies above or on below or on the x-axis. Show your work. y=-x^2-5x      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 171217: Without drawing the given ewuation, determine
A)how many x-intercepts the parabola has
B)whether its vertex lies above or on below or on the x-axis. Show your work.
y=-x^2-5x+6
y=-x^2+2x-1
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-5x%2B6=0 given....... x intercepts are found when y is 0
:
%28x-2%29%28x-3%29 so x intercepts are 2 and 3.
:
vertex (-B/2A , C - B^2/4A) (5/2(1),6-(25/4)...(5/2,-1/4)
so the vertex is below the x axis
:
-x%5E2%2B2x-1=0
vertex for x is -2/2(-1)=1 plug that into equation to find y
:
%28-1%29%5E2%2B2%28-1%29-1=y=0....so vertex is at (1,0) which is on the x axis meaning there is no x intercepts
there is one x intercept at x=1
:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B2x%2B-1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%282%29%5E2-4%2A-1%2A-1=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%282%29%29%2F2%5C-1.
Expression can be factored: -1x%5E2%2B2x%2B-1+=+%28x-1%29%2A%28x-1%29

Again, the answer is: 1, 1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B2%2Ax%2B-1+%29