## kylewendt Group Title How do you graph the quadratic equation 3x^2=3? I need help, my EOC is next Tuesday. 3 months ago 3 months ago

1. TurtleMuffin Group Title

First you can divide both sides by 3 to get x^2 = 1. Subtract 1 from both sides and you have x^2 - 1 = 0. The roots of this are -1 and 1. So this is a standard parabola shifted down one united passing through -1 and 1 on the x-axis.

2. FibonacciChick666 Group Title

first, what shape does the graph make?

3. kylewendt Group Title

The graph makes a parabola when completed

4. FibonacciChick666 Group Title

good, now, that is an important concept, so now, you have one slight problem, This is only in one variable(x) so you can't graph it. Are you sure you copied the question correctly?

5. kylewendt Group Title

Yes. The exact question is: What are the solutions of the equation 3x^2=3? Use a graph of the related function.

6. Hero Group Title

@FibonacciChick666, what do you mean it can't be graphed?

7. FibonacciChick666 Group Title

'graphed' I mean, it's a number line as stated

8. Hero Group Title

Continuing what Turtlemuffin was saying, you have x^2 - 1 = 0 which factors to (x + 1)(x - 1) = 0

9. kylewendt Group Title

My question is, after you have your two x-intercepts, how do you find the vertex from (x+1)(x-1)=0?

10. Hero Group Title

We can use the vertex formula to graph the vertex. $$x = -\dfrac{b}{2a}$$

11. Hero Group Title

In this case b = 0 and a = 1, so $x = -\frac{0}{2(1)} = 0$

12. FibonacciChick666 Group Title

@Hero , one variable= 1-D , no?

13. Hero Group Title

Since $$x = 0$$, we can insert 0 into the expression to get y = $$0^2 - 1 = -1$$ so the vertex is $$(0,-1)$$

14. kylewendt Group Title

So, the graph would look like this?

15. TurtleMuffin Group Title

That is an algebraic approach. You should know the graph of y=x^2. It's the standard parabola. We simplified your given equation into 0 = x^2 - 1. The "minus 1" tells us our standard parabola shifts down one unit. Therefore its x-coordinate remains the same, and it's y-coordinate is shifted down 1 unit from 0, i.e. it's now -1. You can remember all the formulas you want, but if you don't see how an algebraic equation is related to its graphical representation, you won't enjoy math too much. That is has how the graph looks like though!

16. FibonacciChick666 Group Title

ah, now that I re-read the prompt, I understand.

17. FibonacciChick666 Group Title

It wanted the roots, by looking at the related graph

18. kylewendt Group Title

Thank you all for explaining, as I understand this concept now. My algebra teacher is one of the worst (I know that sounds generic), and intentionally ignores my questions to her on assignments because she doesn't like me. This really helps.