Home> Questions>Q 4209
Next
In Process

AcedStudy Latest Questions

acedstud
  • 0
Asked: 2021-03-08T05:00:29+00:00 In: ,

Question of the Day (08/03/2021)

  • 0

The graph of a quadratic equation y=ax^2+bx+c has its roots at x=1 and x=-17. If its vertex is at the point (-8, -81), what are the values of a, b, and c?

quadratic equationquadratic graphroots of quadratic equationvertex of quadratic graph

You must login to add an answer.

Need An Account,

1 Answer

  2. acedstud

    Since the roots are at x=1 and x=-17, the equation is of the form y=a(x-1)(x+17) . . . . . . . .(1)

    Also, since the vertex of the graph is at the point (-8, -81), the vertex form of the quadratic equation is y=a(x+8)^2-81 . . . . . . . .(2)

    Equating equation (1) and (2) gives:

    a(x-1)(x+17)=a(x+8)^2-81

    \Rightarrow a(x^2+16x-17)=a(x^2+16x+64)-81

    \Rightarrow ax^2+16ax-17a=ax^2+16ax+64a-81

    \Rightarrow -17a=64a-81

    \Rightarrow 64a+17a=81

    \Rightarrow 81a=81

    \Rightarrow a=1

    Substituting a=1 into equation (1) gives:

    y=(x-1)(x+17)

    \Rightarrow y=x^2+16x-17

    Therefore, a=1, b=16, and c=-17.

Related Questions