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kylewendt
How do you graph the quadratic equation 3x^2=3? I need help, my EOC is next Tuesday.
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.
first, what shape does the graph make?
The graph makes a parabola when completed
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?
Yes. The exact question is: What are the solutions of the equation 3x^2=3? Use a graph of the related function.
@FibonacciChick666, what do you mean it can't be graphed?
'graphed' I mean, it's a number line as stated
Continuing what Turtlemuffin was saying, you have x^2 - 1 = 0 which factors to (x + 1)(x - 1) = 0
My question is, after you have your two x-intercepts, how do you find the vertex from (x+1)(x-1)=0?
We can use the vertex formula to graph the vertex. \(x = -\dfrac{b}{2a}\)
In this case b = 0 and a = 1, so \[x = -\frac{0}{2(1)} = 0\]
@Hero , one variable= 1-D , no?
Since \(x = 0\), we can insert 0 into the expression to get y = \(0^2 - 1 = -1\) so the vertex is \((0,-1)\)
So, the graph would look like this?
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!
ah, now that I re-read the prompt, I understand.
It wanted the roots, by looking at the related graph
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.