Answer:
The intersection points between the functions are (-4,16) and (2,4)
Step-by-step explanation:
Intersection Between Functions
We are given the functions:
[tex]y=x^2[/tex]
[tex]6x+3y=24[/tex]
To find the intersections between them, we have to solve the system of equations. Let's start by simplifying the second equation by 3:
[tex]2x+y=8[/tex]
Now we substitute [tex]y=x^2[/tex] into this equation:
[tex]2x+x^2=8[/tex]
Solve the quadratic equation by any of the available methods.
Subtract 8:
[tex]2x+x^2-8=0[/tex]
Sort the polynomial:
[tex]x^2+2x-8=0[/tex]
Factor:
[tex](x+4)(x-2)=0[/tex]
Solve:
[tex]x=-4, x=2[/tex]
Now find the y-coordinate of each solution:
[tex]y=x^2=(-4)^2=16[/tex]
The point is (-4,16)
For x=2:
[tex]y=x^2=2^2=4[/tex]
The point is (2,4)
The intersection points between the functions are (-4,16) and (2,4)
