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Question

2. if the graph of the function f(x) = 4x squared - 20x - 4 intersects the graph of the function g(x) = 1 + 4x - x sqaured at the point (m,k), show that the other point of intersection occurs where x = (-1/m).

The asnwer for this question is -23/12. Please give the detailed steps clearly so that i can understand how this answer comes about.

Thanks in advance!

Hey guys..I made a mistake. -23/12 is NOT the answer to this solution. And i dont knw the correct answer now. But u have got to show that x = (-1/m) so i dont think there is a definite answer as u r just proving...rite?

Answer 1

Set the functions equal to each other:

4x^2 - 20x - 4 = 1 + 4x - x^2

Rearrange:
5x^2 - 24x - 5 = 0

You have a quadratic equation. You know one of the roots is m, and you need to show the other one is -1/m.

Given a quadratic equation of the form ax^2 + bx + c = 0, the product of the two roots is always equal to c/a. In this case, c/a = -5/5 = -1, so the two roots r1 and r2 satisfy r1*r2 = -1. Plug in r1=m, and you get r2 = -1/m.

To see why the product of the two roots is always c/a, use the quadratic formula:

r1*r2 = (-b+sqrt(b^2-4ac))/(2a) * (-b-sqrt(b^2-4ac))/(2a) =
(b^2 - (b^2-4ac))/(4a^2) = 4ac/(4a^2) = c/a.

Answer 2

At the intersection:
f(x) = g(x)
or 4x^2 - 20x - 4 = 1 + 4x - x^2
=> 5x^2 - 24x - 5 = 0
=> x^2 - 4.8x - 1 = 0

we can write this equation as
(x-a)(x-b) = 0 with solutions x=a or x=b
with a+b = 4.8
and a x b = -1

if x = a = m is a solution, we obtain from a x b = -1 that x = b = -1/m is also a solution

Answer 3

y1=4x^2-20x-4
y2=1+4x-x^2
y1=y2 at intersection so 4x^2-20x-4=1+4x-x^2
5x^2-24x-5=0
(5x+1)*(x-5)=0 y2=5/25

x=-1/5 and x=5 m is 5 , k=y1=4

Answer 4

huh?