Mathematics

Question

Convert y = x^2 + 2x - 5 into the form y-k = a( x- h)^2

1 Answer

  • Answer:

    [tex]y+6=(x+1)^{2}[/tex]

    Step-by-step explanation:

    we have

    [tex]y=x^{2}+2x-5[/tex]

    This is the equation of a vertical parabola open upward (because the leading coefficient is positive)

    The vertex is a minimum

    The equation of a vertical parabola into vertex form is

    [tex]y-k=a(x-h)^2[/tex]

    where

    (h,k) is the vertex of the parabola

    Convert the equation into vertex form

    Move the constant term to the left side

    [tex]y+5=x^{2}+2x[/tex]

    Complete the square

    [tex]y+5+1=x^{2}+2x+1[/tex]

    [tex]y+6=x^{2}+2x+1[/tex]

    Rewrite as perfect squares

    [tex]y+6=(x+1)^{2}[/tex]

    therefore

    [tex]a=1\\h=-1\\k=-6[/tex]

    The vertex is the point (-1,-6)