Question

Algebra Help Please

1. Solve each equation by graphing the related function. If the equation has no real-number soultion, write no solution.
x^2 - 9 = 0

A) x = +3
B) x = +9
C) x = 0
D) no solution

Answer 1

@DanJS @texaschic101

Answer 2

x^2 will always give a positive value

Answer 3

@DanJS So it could be any of the answers?

Answer 4

So it wants you to graph y=x^2-9. This is a parabolic function with it's vertex starting at (0,-9) and growing upwards. Then you need to find where it is equal to 0, ie where the function hits the x-axis. We can do this by setting x^2-9 equal to 0 and solving for x (this will give us two roots, one the opposite sign of the other).

Do you understand?

Answer 5

Obviously, the answers only include one of the two solutions, so you just have to calculate which one :)

Answer 6

How can I calculate it?

Answer 7

\[x^2-9=0 \rightarrow x^2=9\]
Solve for x.

Answer 8

9x^2

Answer 9

I'm guessing B

Answer 10

Don't guess. Solve it. It's easy.

Answer 11

I dont understand. Can you talk me threw it?

Answer 12

\[x^2=9\]We need to solve for x, but we have x^2. We need to fix that. So how do we reduce the power so that we only have x?
\[\sqrt{x^2}=\sqrt{9} \rightarrow (x^2)^{1/2}=\sqrt{9}\rightarrow x=??\]
What's the square root of 9?

Answer 13

The square root of 9 = 3

Answer 14

@CShrix Is the correct answer A ?

Answer 15

Yes and -3 as well. There are two solutions for x.

Now, the question asks us to solve graphically, but we can use the above to check our work :)

Okay, so how do we solve this graphically?
We can set up a table
x | y
-3 0
-2 -5
-1 -8
0 -9
1 -8
2 -5
3 0

The roots are anywhere where y=0. We see from our table that this is at y=3 and -3.

Checking it again we see that
\[(-3)^2-9=0\]and\[(3^2)-9=0\]

Answer 16

So the answer is really C ?

Answer 17

` We see from our table that this is at y=3 and -3.`
Sorry, I meant where x=3, -3

Answer 18

Oh okay so the answer is A

Answer 19

`The roots are anywhere where y=0. We see from our table that this is at x=3 and -3.`

:)

Answer 20

It's D