Function f(x) = a(x+1)(x-3) has a vertex at (1, -16). Find a.?

Function f(x) = a(x+1)(x-3) has a vertex at (1, -16). Find a.

5 Answers

Relevance
  • 1 month ago

    f(x)=a(x+1)(x-3)

    =>

    -16=a(1+1)(1-3)

    =>

    -16=-4a

    =>

    a=4

  • 1 month ago

    Here's your function:

    f(x) = a(x + 1)(x - 3)

    The vertex is (1, -16), so that means f(1) = -16.

    Just plug in those values and you have:

    -16 = a(1 + 1)(1 - 3)

    It's simple algebra from there. You can do it!

  • 1 month ago

    y = a(x+1)(x-3)

    y = a(x² – 2x – 3)

    y(1/a) = x² – 2x – 3 

    y(1/a) + 4 = x² – 2x + 1 

    y(1/a) + 4 = (x – 1)²

    the x cord of the vertex is indeed at 1

    y cord;

      4p(y–k) = y(1/a) + 4

      k = –16

      4p(y+16) = y(1/a) + 4

      4py + 64p = y(1/a) + 4

    if 64p = 4, p = 4/64 = 1/16

      4p = 1/a

      4/16 = 1/4 = 1/a

      a = 4

    y = a(x² – 2x – 3)

    y = 4(x² – 2x – 3)

    or

    y = 4(x + 1)(x – 3)

    Parabola vertical 

    4p(y–k) = (x–h)² 

    p is distance vertex to focus, if positive opens up 

    p is also distance vertex to directorix 

    vertex at (h, k) 

    Attachment image
  • rotchm
    Lv 7
    1 month ago

    You are told that -16 = a(1+1)(1-3). Convince yourself of this.

    Now, can you solve for "a" ? Done!

    Hopefully no one will spoil you the answer thereby depriving you from your personal enhancement; that would be very inconsiderate of them. 

  • How do you think about the answers? You can sign in to vote the answer.
  • 1 month ago

    You are given the function and a point, which includes x and y.  Substitute and solve for the unknown:

    f(x) = a(x + 1)(x - 3)

    x = 1

    f(x) = -16

    -16 = a(1 + 1)(1 - 3)

    -16 = a(2)(-2)

    -16 = -4a

    4 = a

Still have questions? Get your answers by asking now.