Is this first step correct?

[pinkcalculator]

The line l passes through the two points of intersection of the graphs of f(x)= -x squared +ax+2 and g(x)= ax squared + 7x-6. One of these points occurs at x= -2. Find the equation of the line l.

So I started by substituting x= -2 into the functions.
-(-2)squared + a(-2) + 2 = 0
-4 -2a =0
a= -1.

a(-2) squared +7(-2) -6
4a -20=0.
a= 5.

Is it okay that I set the functions to zero? I don't wanna get to far into the problem if the first part is wrong. If that's right, should I graph them next? I'm a bit lost, but I know that when I graph it, I'm going to have three equations.

 

[Deleted member 4993]

The line l passes through the two points of intersection of the graphs of f(x)= -x squared +ax+2 and g(x)= ax squared + 7x-6. One of these points occurs at x= -2. Find the equation of the line l.

So I started by substituting x= -2 into the functions.
-(-2)squared + a(-2) + 2 = 0 ? Why is this equal to 0?
-4 -2a =0
a= -1.

a(-2) squared +7(-2) -6
4a -20=0.? Why is this equal to 0?
a= 5.

x = -2 is property of one of the points of intersection. The values of 'a' should be equal in these two functions
Is it okay that I set the functions to zero? No - unless you are required to so, like while finding x-intercept, etc.


I don't wanna get to far into the problem if the first part is wrong. If that's right, should I graph them next? I'm a bit lost, but I know that when I graph it, I'm going to have three equations.

f(x) = -x[sup:229h7dsg]2[/sup:229h7dsg] + ax + 2

g(x) = ax[sup:229h7dsg]2[/sup:229h7dsg] + 7x - 6

since they intersect at x = -2 ? f(-2) = g(-2)

-(2[sup:229h7dsg]2[/sup:229h7dsg]) + a(-2) + 2 = a(-2)[sup:229h7dsg]2[/sup:229h7dsg] + 7(-2) - 6

-4 -2a +2 = 4a - 14 - 6

4a + 2a = 18

a = 3

so

f(x) = -x[sup:229h7dsg]2[/sup:229h7dsg] + 3x + 2

g(x) = 3x[sup:229h7dsg]2[/sup:229h7dsg] + 7x - 6

You need to visualize the problem - start with an approximate sketch.

 

[pinkcalculator]

I don't know why I felt the need to set the functions to zero. Probably because I had no idea what to do with them or the information that an intersection was at x= -2.
Graphing did help, a lot.
I was able to graph both functions and found that (1, 4) and (-2, -8) were the two points of intersection. Then I used point slope and now I think I've got it!
Thank you for putting me in the right direction!