SOLUTION: i need help and a couple of things explained better if possible this is what my textbook says: By drawing a suitable graph, find the roots of these quadratic functions. Check e

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: i need help and a couple of things explained better if possible this is what my textbook says: By drawing a suitable graph, find the roots of these quadratic functions. Check e      Log On


   



Question 282540: i need help and a couple of things explained better if possible
this is what my textbook says:
By drawing a suitable graph, find the roots of these quadratic functions. Check each root by substitution:
this is what we have been told to find by our teacher
where does x²-x=0 cut the y-intercept
where it cuts the x-axis
locate the turning point (an axis of symmetry)
i dont know how to do any of it so there is nothing i can write to show what i have done so far ?
thanks if you get back to me x

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
There are some problems with your wording.
x^2-x=0
x*(x-1)=0
the two roots are x=0 and x=1
that is where the parabola crosses the x axis
(0,0) and (1,0)
x intercept is when y =zero the zeroes or roots of the equation
y intercept is when x=0
Nothing cuts the y intercept. Perhaps you want to know the y intercept where x=0 or where it cuts(crosses) the y axis.
1/2^2-1/2
1/4-1/2=-1/4
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B0+=+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=%28-1%29%5E2-4%2A1%2A0=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+1
x%5B2%5D+=+%28-%28-1%29-sqrt%28+1+%29%29%2F2%5C1+=+0

Quadratic expression 1x%5E2%2B-1x%2B0 can be factored:
1x%5E2%2B-1x%2B0+=+1%28x-1%29%2A%28x-0%29
Again, the answer is: 1, 0. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B0+%29