1. ## Solving Quadratic Equations by Graphing

I am having so much difficulty understand this! I have had my teacher explain this and the tutor, and I still don't get it.

1) x²-9=0

How do I solve this? Please tell me step by step.

2. ## Re: Solving Quadratic Equations by Graphing

1) x²-9=0

How do I solve this?
Just replace the 0 with y, so the equation becomes

y = x^2 - 9

This graphs as a parabola with vertex at (0,-9) and x-intercepts at (-3,0) and (3,0). The x values at the intercepts are the solutions to the original equation. This is the graphical method of solving.

The algebraic method is to simply factor and solve:

x^2 - 9 = 0
(x + 3)(x - 3) = 0
x = 3 OR x = -3

Hope that helps.

3. ## Re: Solving Quadratic Equations by Graphing

$x^2-9 \ = \ 0$

$x^2 \ = \ 9$

$\sqrt{x^2} \ = \ \sqrt9$

$|x| \ = \ 3$

$x \ = \ \pm3$

$See \ graph$

[attachment=0:3ryrv9dj]zfg.jpg[/attachment:3ryrv9dj]

4. ## Re: Solving Quadratic Equations by Graphing

Originally Posted by BigGlenntheHeavy
$x^2-9 \ = \ 0$

$x^2 \ = \ 9$

$\sqrt{x^2} \ = \ \sqrt9$

$|x| \ = \ 3$

$x \ = \ \pm3$

$See \ graph$

[attachment=0:1yuyuxjb]zfg.jpg[/attachment:1yuyuxjb]
Thanks^^ The only thing is I just don't understand how to graph the points. And my answer comes in zeros.

5. ## Re: Solving Quadratic Equations by Graphing

$f(x) \ = \ x^2-9$

$f(3) \ = \ 0$

$f(-3) \ = \ 0$

$Hence, \ solutions \ are \ (3,0),(-3,0) \ to \ graph \ of \ f(x) \ = \ x^2-9$

$Or \ manually \ graph \ f(x) \ and \ see \ where \ the \ graph \ intercepts \ the \ x-axis.$

$At \ that \ point \ y \ = \ 0, \ so \ we \ found \ a \ solution \ of \ f(x)$

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