Question

What are the intersections between the lines y=x squared and 6x + 3y= 24?

Answer 1

The intersection points between the functions are (-4,16) and (2,4)

Explanation:

Intersection Between Functions

We are given the functions:

`y=x^2`

`6x+3y=24`

To find the intersections between them, we have to solve the system of equations. Let's start by simplifying the second equation by 3:

`2x+y=8`

Now we substitute
`y=x^2` into this equation:

`2x+x^2=8`

Solve the quadratic equation by any of the available methods.

Subtract 8:

`2x+x^2-8=0`

Sort the polynomial:

`x^2+2x-8=0`

Factor:

`(x+4)(x-2)=0`

Solve:

`x=-4, x=2`

Now find the y-coordinate of each solution:

`y=x^2=(-4)^2=16`

The point is (-4,16)

For x=2:

`y=x^2=2^2=4`

The point is (2,4)

The intersection points between the functions are (-4,16) and (2,4)