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kylewendt

  • 7 months ago

How do you graph the quadratic equation 3x^2=3? I need help, my EOC is next Tuesday.

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  1. TurtleMuffin
    • 7 months ago
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    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
    • 7 months ago
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    first, what shape does the graph make?

  3. kylewendt
    • 7 months ago
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    The graph makes a parabola when completed

  4. FibonacciChick666
    • 7 months ago
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    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
    • 7 months ago
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    Yes. The exact question is: What are the solutions of the equation 3x^2=3? Use a graph of the related function.

  6. Hero
    • 7 months ago
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    @FibonacciChick666, what do you mean it can't be graphed?

  7. FibonacciChick666
    • 7 months ago
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    'graphed' I mean, it's a number line as stated

  8. Hero
    • 7 months ago
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    Continuing what Turtlemuffin was saying, you have x^2 - 1 = 0 which factors to (x + 1)(x - 1) = 0

  9. kylewendt
    • 7 months ago
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    My question is, after you have your two x-intercepts, how do you find the vertex from (x+1)(x-1)=0?

  10. Hero
    • 7 months ago
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    We can use the vertex formula to graph the vertex. \(x = -\dfrac{b}{2a}\)

  11. Hero
    • 7 months ago
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    In this case b = 0 and a = 1, so \[x = -\frac{0}{2(1)} = 0\]

  12. FibonacciChick666
    • 7 months ago
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    @Hero , one variable= 1-D , no?

  13. Hero
    • 7 months ago
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    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
    • 7 months ago
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    So, the graph would look like this?

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  15. TurtleMuffin
    • 7 months ago
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    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
    • 7 months ago
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    ah, now that I re-read the prompt, I understand.

  17. FibonacciChick666
    • 7 months ago
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    It wanted the roots, by looking at the related graph

  18. kylewendt
    • 7 months ago
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    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.

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