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anonymous

  • one year ago

An expression is shown below: f(x) = –16x2 + 22x + 3 Part A: What are the x-intercepts of the graph of the f(x)? Show your work. (2 points) Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points) Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)

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  1. anonymous
    • one year ago
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    I can help with Part A only. :( Is that okay or you need some more talented guy to solve all the three for you? :P

  2. anonymous
    • one year ago
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    that's fine

  3. anonymous
    • one year ago
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    Okay, f(x) or y both are one and same thing, so you have : \(y = -16x^2 + 22x + 3\)

  4. anonymous
    • one year ago
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    See, to find x-intercept, you put y = 0.. And to find y-intercept (if someone asks you to), then you put x = 0..

  5. anonymous
    • one year ago
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    So, here you need to find x-intercept, so you put y = 0, so you have: \(y = -16x^2 + 22x + 3\) \(\implies 0 = -16x^2 + 22x + 3\)

  6. anonymous
    • one year ago
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    All good till here?

  7. anonymous
    • one year ago
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    sorta then what would you do

  8. anonymous
    • one year ago
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    Then now you have got a quadratic equation to solve, solve for x there..

  9. SolomonZelman
    • one year ago
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    Part B: the vertex is: maximum with negative leading coefficient. minimum with positive leading coefficient. to find the vertex, complete the square.

  10. anonymous
    • one year ago
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    Actually, x-intercept is the point where your graph cuts x-axis, and on x-axis, you have only x values, there y = 0..

  11. anonymous
    • one year ago
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    That is why we put y = 0 to find x-intercept.. @SolomonZelman will tell you the next two parts. Just solve the quadratic equation to find x..

  12. SolomonZelman
    • one year ago
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    told part B already.... ---------------------------------- For part C: Use the x-intercepts (you can also use the y-intercept which is simple to find -- optional) And for \("\)Justify that you can use the answers obtained in Part A and Part B to draw the graph.\("\) it is justified, but your graph of course won't look and be exact as on a graphing calculator.

  13. SolomonZelman
    • one year ago
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    Do you want to tell me right now, if your vertex is maximum or minimum ?

  14. anonymous
    • one year ago
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    yes please

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