anonymous
  • anonymous
Write the equation of the quadratic function with roots -2 and 4 and a vertex at (1, 9).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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welshfella
  • welshfella
the vertex form of a quadratic is a(x - h)^2 + k where the vertex is at (h,k)
welshfella
  • welshfella
so in your case we have f(x) = a(x - 1)^2 + 9
welshfella
  • welshfella
now you need to find the value of a which you can do using the given roots

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anonymous
  • anonymous
so what is a?
welshfella
  • welshfella
a is a number to be found
welshfella
  • welshfella
the roots are -2 and 4 so points of intersection on x-axis are (-2,0) and (4,0) So plugging these values into the above equation and solving for a will give you the final equation
anonymous
  • anonymous
I'm really not good at this. but i think i'm kinda getting it? could you just show me please?
welshfella
  • welshfella
ok f(x) = 0 when a - -2 so 0 = a(-2-1)^2 + 9 0 = 9a + 9 -9a = 9 a = -1 so we;ve found a
anonymous
  • anonymous
so the answer is f(x) = -1(x - 1)^2 + 9?
welshfella
  • welshfella
yes
anonymous
  • anonymous
thanks so much. i will fan and medal you. :)
welshfella
  • welshfella
they might want it in standard form though just expand and simplify
welshfella
  • welshfella
yw ty
welshfella
  • welshfella
they haven't asked for that so leaving in in the above form should be ok
anonymous
  • anonymous
yep, that should be fine. thanks again.

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