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

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) (Show Source): You can put this solution on YOUR website!
given....... x intercepts are found when y is 0
:
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
:

vertex for x is -2/2(-1)=1 plug that into equation to find 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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=0 is zero! That means that there is only one solution: .
Expression can be factored:

Again, the answer is: 1, 1. Here's your graph:

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