SOLUTION: Please help me! Cannot figure this out. it says: without drawing the graph of the given equation,determine a)how many x-intercepts the parabola has b)whether its vertex lies above

Algebra ->  Functions -> SOLUTION: Please help me! Cannot figure this out. it says: without drawing the graph of the given equation,determine a)how many x-intercepts the parabola has b)whether its vertex lies above       Log On


   

Question 131282This question is from textbook structure and method
: Please help me! Cannot figure this out. it says: without drawing the graph of the given equation,determine a)how many x-intercepts the parabola has b)whether its vertex lies above or below or on the x-axis.
y=-x^2+2x-1
Please and THank you=) This question is from textbook structure and method

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The equation is in the form y+=+ax%5E2+%2B+bx+%2B+c
a+=+-1
b+=+2
c+=+-1
The vertex will be at (-(b/2a), y) where you figure out the
x-coordinate first, then figure out the y-coordinate
-%28b%2F2a%29+=+-%282%2F%282%2A%28-1%29%29%29
-%28b%2F2a%29+=+-2%2F-2
-%28b%2F2a%29+=+1
Now plug x+=+1 into the equation to find the y-coordinate
of the vertex.
y+=+-x%5E2+%2B+2x+-+1
y+=+-%281%29%5E2+%2B+2%2A1+-+1
y+=+-1+%2B+2+-1
y+=+0
So, the vertex is at (1,0), which means it touches the x-axis
at 1 point only
Because a is negative, the parabola opens down, like a cup
spilling out it's water. Therefore it lies below the x-axis
I'll graph it just to make sure
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+3%2C+-x%5E2+%2B+2x+-+1%29+