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kassia

Which one of these equations would make a graph with a downward facing parabola with an x intercept of 3 and a y intercept of 3 y+1=-(x-4)^2; y= -x^2+3x-4; y=(x+1)(x-3); y=-(x+1)(x-3)

  • 2 years ago
  • 2 years ago

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  1. AntiMatter
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    All right, when you graph the function \[y=x^{2}\] you get a parabola, centered at the origin, it faces up

    • 2 years ago
  2. LagrangeSon678
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    solved it, go to you original post

    • 2 years ago
  3. AntiMatter
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    so here you have 4 equations

    • 2 years ago
  4. AntiMatter
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    \[y+1=-(x-4)^2\] \[y= -x^2+3x-4\] \[y=(x+1)(x-3)\] \[y=-(x+1)(x-3)\]

    • 2 years ago
  5. kassia
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    i saw that you solved it for a second and then the computer im on decided to be uncoperative so i can no longer view it is it possible for you to copy and paste sorry for the hassle

    • 2 years ago
  6. LagrangeSon678
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    yeah hold on

    • 2 years ago
  7. LagrangeSon678
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    The answer to your question is : y=-(x+1)(x-3). Why? becuase from the factored form we see that there will be an xintercept at (3,0). TO get the y intercept you have to replace x with zero and evluate. you will get (0,3).

    • 2 years ago
  8. AntiMatter
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    you want an x intercept of 3, therefore then y=0, the function will x will be 3

    • 2 years ago
  9. LagrangeSon678
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    Also we know this a downward facing parabola because of the negative sign

    • 2 years ago
  10. kassia
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    so how do you tell which equation will make what type of parabola?

    • 2 years ago
  11. LagrangeSon678
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    Will a downward facing parabola should have a negative sign on the leading term. It is best to expand y=-(x+1)(x-3), You should get y=-x^2-2x-3

    • 2 years ago
  12. LagrangeSon678
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    now that you have this expaned, you can see that this indeed will be a parabola because of the x^2 term. Then you also have the factored form. To get the x and y intecepts, in this case, it is good to use the factored from. To get y-int set x to be zero and solve. To get x-intercpet set y to be zero and solve.

    • 2 years ago
  13. AntiMatter
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    so starting with \[y=x^2\] we can transform this into the equation we want. so y intercept of 3, that means when x = 0 the function will equal 3, therefore, consider the basic parabola, \[3=(0^2)\], so you need to add 3 therefore it becomes \[y=x^2 + 3\]

    • 2 years ago
  14. kassia
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    thanks guys!

    • 2 years ago
  15. AntiMatter
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    now consider the x intercept of 3, that means when y=0, the function will equal 3.... we now have \[y=x^2+3\]

    • 2 years ago
  16. AntiMatter
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    we want this function to me moved to the right 3 units

    • 2 years ago
  17. AntiMatter
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    sorry, this isn't the right approach, let's just analyze the given functions, however, it seems your question was already answered

    • 2 years ago
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