SOLUTION: Without drawing a graph how can I determine (a) how many x-intercepts the parabola has (b) whether its vertex is above, below or on the x- axis? y = -x^2 + 2x-1

Question 7460: Without drawing a graph how can I determine (a) how many x-intercepts the parabola has (b) whether its vertex is above, below or on the x- axis?

y = -x^2 + 2x-1
Answer by ichudov(507) (Show Source): You can put this solution on YOUR website!
x intercepts is just another way of saying "roots". Find roots of this quadratic expression with y set to 0.
since coefficient in front of x is negative, the parabola is pointing downwards.
where its vertex is, depends on the roots.

Solved by pluggable solver: SOLVE quadratic equation with variable

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:

since both roots are same, its vertex is right on the x axis.
RELATED QUESTIONS
Without drawing the graph of the given equation, determine (a) how many x-intercepts the... (answered by mmm4444bot)

Without drawing the graph of the given equation, determine (a) how many x-intercepts the... (answered by mmm4444bot)

This is a parabola question. I really need help solving. if you could please show me the... (answered by richwmiller,drk)

Without drawing the graph determine how many x- intercepts the parabola has and whether... (answered by jsmallt9)

Without drawing the graph determine how many x- intercepts the parabola has and whether... (answered by jsmallt9,jojo14344)

Please help me! Cannot figure this out. it says: without drawing the graph of the given... (answered by solver91311)

Please help me! Cannot figure this out. it says: without drawing the graph of the given... (answered by josmiceli)

It asks, without drawing the graph of the given equation, determine: How many... (answered by jim_thompson5910,mangopeeler07)

Without drawing the given ewuation, determine A)how many x-intercepts the parabola has (answered by Mathtut)