Question

I need help I have no idea if i am doing this right.
The question says solve the equation algebraically and graphically.
V^2-5=8-2v^2
my final answer was v=√13. Is that right and how would I solve it graphically

Answer 1

V^2-5=8-2v^2

I would combine the v^2 terms: add +2V^2 to both sides
V^2 + 2V^2 - 5 =8 -2V^2 + 2V^2
on the right side, -2V^2 + 2V^2 is 0 (you have 2 V^2 and take way 2 V^2 to get no V^2 )
on the left you have 3 V^2 so you have
3 V^2 -5 =8

now add +5 to both sides. you get
3 V^2 = 13
divide both sides by 3
V^2 = 13/3

now take the square root of both sides
V= \( \pm \sqrt{\frac{13}{3} } \)

Answer 2

notice you get 2 answers, either plus or minus the square root of 13/3

Answer 3

to solve it graphically, we could do this

let V be x (because I always use x and y for graphs)

3V^2 = 13 becomes

3x^2=13
we could write this as
3x^2-13 =0

we can make this a function of x by saying
y= 3x^2 -13
and solving for x when y =0
or we can graph the function, and look at the graph for where the function crosses the x-axis (i.e. where y=0)

to graph this function, try some small numbers near zero:
say x= -2, -1, 0 , 1 ,2
figure out the y values. plot the points, connect the dots