Graph the equations to find the solution(s) to the system. y=x+2y=12(x+3)(x−5) Use the Line tool to graph the line. Use the Parabola tool to graph the parabola

Answer 1

y=x + 2y = 12(x+3)(x-5)

is a little ambiguous.

Maybe you mean

y =x+2y

and

y = 12(x+3)(x-5)

1st equation is the same as

-y=x

y = -x

which is a straight line through the origin, with slope =-1

2nd equation is

an upward opening parabola

the solution is where the line and parabola intersect

y=-x

y = 12(x+3)(x-5)

= 12(x^2 -2x -15)

= 12x^2 -24x -180

set them equal

-x = 12x^2 -24x -180

12x^2 -23x -180 = 0

use the quadratic formula

x =23/24 + or - (1/24)sqr(23^2 +48(180))

solve for x

x=about (23+or- 95.755)/24

x = about 118.755/24 or - 72.755/24

x = about 4.95 or -3.03

y=-x= about -4.95 or 3.03

solutions are (-3.03, 3.03) and (4.95, -4.95)

intersections of the line and curve in quadrants II and IV

or use a graphing calculator

check the solution

12(-3.03)^2-23(-3.03)-180= about 110+70-180= 0

Answer 2

Hi Jesus!

This sounds like a tricky problem, but it truly is asking you to visualize these equations. I would recommend looking up Desmos Grapher and plugging the formulas in to complete this assignment. I have created a Desmos Graph for you to look at as well. It can be found here: https://www.desmos.com/calculator/c2ggh3mscl .

Best,

Peyton