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egracer

  • one year ago

The equation f(x) = 5x2 − 30x + 6 represents a parabola. What is the vertex of the parabola? (−5, 281) (5, −19) (−3, 141) (3, −39)

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  1. anonymous
    • one year ago
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    In the general equation of a parabola\[f \left( x \right) = ax ^{2} + bx + c\]The x-coordinate of the vertex is given by\[x=-\frac{ b }{ 2a }\]Then calculate f(x) using this value of x to give you the y-coordinate of the vertex.

  2. egracer
    • one year ago
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    Would it be B?

  3. anonymous
    • one year ago
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    Don't think so.

  4. egracer
    • one year ago
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    Sorry trying to figure this out haha math isn't my best subject so its a little harder let me try to recalculate

  5. anonymous
    • one year ago
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    No problem. Take your time. What do you get for the x-coordinate? (-b/2a)

  6. egracer
    • one year ago
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    would the x coordinate be -39/2a?

  7. anonymous
    • one year ago
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    Not quite. From looking at the given quadratic, what is the value of a and the value of b?

  8. anonymous
    • one year ago
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    a multiplies x^2 and b multiplies the x

  9. egracer
    • one year ago
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    honestly I have no clue I'm so confused on how to do this could you explain like in details like how to solve it

  10. anonymous
    • one year ago
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    I just did. But let's back up. The given quadratic function is\[f \left( x \right) = 5x ^{2} - 30x + 6\]Compare that with\[f \left( x \right) = ax ^{2} + bx + c\]a is the number that multiplies x^2 b is the number that multiplies x What are they?

  11. egracer
    • one year ago
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    a is 5 and b is -30??

  12. anonymous
    • one year ago
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    Perfect. Now the x-coordinate is given by\[x = -\frac{ b }{ a }\]Plug in those values of a and b . What do you get?

  13. anonymous
    • one year ago
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    Sorry. It's\[x=-\frac{ b }{ 2a }\]

  14. anonymous
    • one year ago
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    So you're calculating\[x=-\frac{ b }{ 2a } = -\frac{ -30 }{ 2\left( 5 \right) } = ?\]

  15. egracer
    • one year ago
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    -75?

  16. anonymous
    • one year ago
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    Nope. What is 2 x 5 ?

  17. egracer
    • one year ago
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    10

  18. anonymous
    • one year ago
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    Good. That's the denominator. Now, what's -30/10 ?

  19. egracer
    • one year ago
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    -3

  20. anonymous
    • one year ago
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    Good. Finally, what's -(-3) ?

  21. egracer
    • one year ago
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    3

  22. anonymous
    • one year ago
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    Excellent. So the x-coordinate of the vertex is 3.

  23. anonymous
    • one year ago
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    Now, to get the y-coordinate of the vertex, put his value of x into the original function and calculate f(3)\[f \left( x \right)=5x ^{2}-30x+6\]\[f \left( 3 \right) = 5\left( 3 \right)^{2}-30\left( 3 \right) + 6\]What do you get?

  24. egracer
    • one year ago
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    -18?

  25. anonymous
    • one year ago
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    Nope. What is 3^2 ?

  26. egracer
    • one year ago
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    9

  27. anonymous
    • one year ago
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    Great. Now what is 5 x 3^2 ?

  28. egracer
    • one year ago
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    45

  29. anonymous
    • one year ago
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    Good. Now what is 30 x 3 ?

  30. egracer
    • one year ago
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    90

  31. anonymous
    • one year ago
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    Great. Now to put it all together\[f \left( 3 \right) = 5\left( 3 \right)^{2} - 30\left( 3 \right) + 6 = 45-90+6 = ?\]

  32. egracer
    • one year ago
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    -39

  33. anonymous
    • one year ago
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    Good. Now you have the x- and y-coordinates of the vertex. Where is the vertex?

  34. egracer
    • one year ago
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    3,-39 is my answer?

  35. anonymous
    • one year ago
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    That's it. Well done.

  36. egracer
    • one year ago
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    thank you so much for being patient with me! and helping me understand!

  37. anonymous
    • one year ago
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    You're welcome. Good luck with your studies.

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