Maths...graph and parabola..PLEASE HELP. Give 10 points for best answer!?

Question

The diagram below (can't show it) shows the fraph of the line
y=2x-4 and the parabola y=x^2+x-2

Question: The x intercepts can be found by solving the quadratic equation x^2+x-2=0

Use your knowledge of the two x intercepts to write down the values of c and d.
Thankyou!

Answer 1

The parabola y= x^2 + x - 2 = (x+2)(x-1) has x- intercepts at
x = -2 and x = 1. The parabola has a minimum at x=-1/2. Its value is y=(-1/2)^2 -1/2 -2 = 1/4 -1/2 -2 = -2 1/4. So the vertex of the parabola is at (-1/2, - 2 1/4).

The equation of the line is y= 2x-4, So intersection occurs when
x^2 +x -2 = 2x-4
x^2-x +2 =0
This equation has imaginary roots and so line does not intersect the parabola.

I was hoping that c and d were the points where the line intersected the parabola, but that's not the case.

Too bad.

Answer 2

If line and the parabola intersect, then the following is true:

2x - 4 = x^2 + x - 2 (using the equations that are given)
0 = x^2 - x + 2

the quadratic equation:
x = (-b +/- sqrt(b^2 -4ac)) / 2a
x = (1 +/- sqrt (-7)) / 2
this is imaginary, so the line and the parabola do not intersect.

However in the second part of the question you give the equation: x^2+x-2=0 (which is not the correct equation that needs to be solved but on the other had gives real numbers):

x = (-1 +/- sqrt(1+8)) / 2
x = +1 or - 2

however if you input this into the equations, the Y values differ when they should be the same.

The answer: the line and the parabola do not intersect or the original equations given are wrong.

Answer 3

what is c and d???

if c and d are x intercepts,
y = y
x^2 + x - 2 = 0 > because x axis is y = 0
(x+2)(x-1) = 0
x = -2 x =1

if c and d are interception between line and parabola,
y = y
x^2 + x - 2 = 2x -4 > because line is y=2x - 4
x^2 + x - 2x - 2 + 4 = 0
x^2 - x + 2 = 0
line and parabola never cross / touch since there are no real factors...

Answer 4

You can graph your functions on this website, if you don't have a graphing calculator:
http://www.coolmath.com/graphit/index.html

The parabola crosses the x axis twice, at x = -2 and x = 1. The corresponding factors are (x+2) and (x-1). The line crosses it once, at x = 2.

Answer 5

factored it would be (x+2)(x-1) so the x intercepts are at -2 and 1 if that helps c and d have no relevance in the question.

Answer 6

Kentucky Boy has more advantageous tooth than the finished city . each and anybody interior the small city of Doubledown, KY are out to shoot to kill Bubba Bitesdouble for his tooth, although the interior sight city Sheriff will hunt him down first.

Answer 7

Kind of hard when we can't see the graph.

Answer 8

there's no c and d anywhere in the task