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anonymous

  • one year ago

I need to find the equation ax^2+bx+c using the points (5,2) (6,1) (4,1). I have no clue how to do it. I will give medal to everyone that helps.

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  1. kropot72
    • one year ago
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    First you need to use the ordered pairs to set up 3 equations. Then the equations must be solved to find the values of a, b and c.

  2. anonymous
    • one year ago
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    i have no clue how to do that

  3. kropot72
    • one year ago
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    To form the 3 equations, the values in the ordered pairs are plugged into the equation for the quadratic: 25a + 5b + c = 2 ........(1) 36a + 6b + c = 1 ........(2) 16a + 4b + c = 1 ........(3) Now solve these equations to find the values of a, b and c.

  4. anonymous
    • one year ago
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    this the the graph

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  5. anonymous
    • one year ago
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    i still dont understand

  6. anonymous
    • one year ago
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    i also need to find the x and y intercpets of that parabola along with the equation but i have no clue how to do it

  7. anonymous
    • one year ago
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    kropot you there?

  8. kropot72
    • one year ago
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    If we subtract equation (1) from equation (2) we can eliminate c as follows: 11a + b = -1 ...........(4) And if we subtract equation (3) from equation (2) we get another equation in a and b as follows: 20a + 2b = 0 ............(5) Multiplying equation (4) by 2 gives: 22a + 2b = -2 ..........(6) Subtracting (5) from (6) we get: 2a = -2 ....................(7) which gives a the value of -1.

  9. anonymous
    • one year ago
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    can you help me find the x and y intercepts

  10. kropot72
    • one year ago
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    Put y equal to zero. Then use the formula for solving any quadratic to find the two values of x.

  11. anonymous
    • one year ago
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    and that is the equation for that parabola using the 3 points i said above?

  12. anonymous
    • one year ago
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    i dont know how to use the quadratic formula, very well

  13. kropot72
    • one year ago
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    By substitution in (4) we find the value of b is 10. And by substitution in (3) the value of c is found to be -23. The required equation is therefore: \[\large -x^{2}+10x-23\]

  14. anonymous
    • one year ago
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    i still have no clue how to find them

  15. kropot72
    • one year ago
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    "and that is the equation for that parabola using the 3 points i said above?" Yes, it is. You had better do some work on the formula for solving any quadratic, and then solve it yourself. I shouldn't have to do all your work :)

  16. anonymous
    • one year ago
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    so -23 would be my y-intercept correct?

  17. kropot72
    • one year ago
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    To find point C on the graph you need to find the value of the quadratic when x = 5.

  18. anonymous
    • one year ago
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    and how exactly do i do that?

  19. kropot72
    • one year ago
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    Yes, the intercept on the y-axis is at y = -23.

  20. anonymous
    • one year ago
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    so now that i have my y-intercept how do i find my x-intercept?

  21. kropot72
    • one year ago
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    Solve the quadratic \[\large -x^{2}+10x-23=0\] using \[\large x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\]

  22. kropot72
    • one year ago
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    To find point C on the graph you need to find the value of the quadratic when x = 5. Just plug the value x = 5 into \[\large y=-x^{2}+10x-23\]

  23. anonymous
    • one year ago
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    so the x-intercept is 2?

  24. anonymous
    • one year ago
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    when i pulgged x into the equation i got y=-5^2+10(5)-23

  25. kropot72
    • one year ago
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    The ordered pair for point C on the graph is (5, 2). Just look at the graph to see that it is the coordinates for the highest point.

  26. anonymous
    • one year ago
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    so am i right about the x-inttercept?

  27. kropot72
    • one year ago
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    The intercepts on the x-axis are found by using the formula for solving any quadratic and putting y = 0. The x-intercept is not 2.

  28. anonymous
    • one year ago
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    but thats what i got when i plugged it into the equation

  29. kropot72
    • one year ago
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    The intercepts on the x-axis are found from \[\large x=\frac{-10\pm \sqrt{8}}{-2}\]

  30. anonymous
    • one year ago
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    the answer i got is definetly not right

  31. anonymous
    • one year ago
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    i got 5+-sqrt2

  32. kropot72
    • one year ago
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    What is the answer then?

  33. anonymous
    • one year ago
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    5?

  34. anonymous
    • one year ago
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    im not sure, im really bad at math

  35. kropot72
    • one year ago
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    How do you know that the result for the intercepts on the x-axis being 5 +-square root 2 is not right?

  36. kropot72
    • one year ago
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    That result checks out for me.

  37. anonymous
    • one year ago
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    so its right?

  38. kropot72
    • one year ago
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    Yes.

  39. anonymous
    • one year ago
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    Once the graphed parabola matches as close as possible to the image, make note of the quadratic equation, both in general and standard form (y = ax2 + bx + c). When completed, the graphed parabola should lie on top of the parabola in your image. If necessary, right-click on the image and go to the Color tab to make the image more transparent so the graphed parabola can be seen over the image. The equation is: y=-x^2+10x-23 Image of the Preferences window with the Color tab active. A scale from 0 to 100 is shown. At 0, the image is transparent. At 100, the image is solid. Identify the vertex, axis of symmetry, domain and range of the graphed parabola by inspecting your graph. Vertex: (5,2) Axis of Symmetry: x=5 Find the x- and y-intercepts of the parabola using the "Intersect Two Objects" icon image of geogebra intersect two objects button. Remember this tool may be hidden below other buttons. To find the x-intercepts, select the parabola, then the x-axis. To find the y-intercepts, select the parabola, then the y-axis. X-intercepts: (,) Y-intercepts: (-23) this is what im stuck on

  40. anonymous
    • one year ago
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    but the way that says it makes it seem like it should be points but im not sure

  41. kropot72
    • one year ago
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    Try the values 3.586 and 6.414 for the intercepts on the x-axis.

  42. anonymous
    • one year ago
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    and -23 for the y?

  43. kropot72
    • one year ago
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    Yes.

  44. kropot72
    • one year ago
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    The intercepts on the x-axis are at (3.586, 0) and (6.414, 0) and the intercept on the y-axis is at (0, -23).

  45. anonymous
    • one year ago
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    okay thank you so much for you help, ill give you a medal. i am starting to understand it now. whats your email so i can email you if i have any other questions?

  46. kropot72
    • one year ago
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    You're welcome. Please post any more questions on OS. You can tag me if you like.

  47. anonymous
    • one year ago
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    okay thank you!

  48. hlambach
    • one year ago
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    If this is answered, close the question, please. :)

  49. kropot72
    • one year ago
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    You're welcome :)

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