Question

Solve each equation by graphing both sides of the equation or inequality

6. -3x^2+9
7. (x-2)^2-10 ≤ (x-6)^2-2

Answer 1

see below

Explanation:

6.
`-3x^2+9=-3`

`-3x^2 =-12`

`x^2=4`

`x=` ±
`2`

Solution:
`x=2, x=-2`

Points of intersection: (2, -3) and (-2, -3)

7.
`(x-2)^2-10\leq (x-6)^2-2`

`x^2-4x+4-10\leq x^2-12x+36-2`

`-4x-6\leq -12x+34`

`8x\leq 40`

`x\leq 5`

Solution:
`x\leq 5`

Point of intersection is (5, -1)