solving quadratic equations by graphing

Question

Two numbers have a sum of 2 and a product of -8. The quadratic equation -n^2 + 2n + 8 = 0 can be used to determine the two numbers.

a. Graph the related function f(n) = -n^2 + 2n + 8 and determine its x-intercepts.

b. What are the two numbers?

Answer 1

ANSWER: -2 and 4

 

There are no means by which to show the graph in this forum.

 

When you graph the equation, you will see the x-intercepts are -2 and 4

 

-2 and 4 are the two numbers

 

Alternatively you could factor the equation. To do this first multiply both sides by -1 to get rid of the negative side in front of the first coefficient

 

n^2-2n-8=0

 

Now factor the equation

 

(n-4)(n+2)=0

 

For the above equation to be true, n-4 must be zero or n+2 must be zero. Set these equal to zero and solve

 

n-4=0 so n=4

 

n+2=0 so n=-2

 

And 4 and -2 are your answers