Convert y = x^2 + 2x  5 into the form yk = a( x h)^2
Mathematics
Liitchii
Question
Convert y = x^2 + 2x  5 into the form yk = a( x h)^2
1 Answer

1. User Answers calculista
Answer:
[tex]y+6=(x+1)^{2}[/tex]
Stepbystep explanation:
we have
[tex]y=x^{2}+2x5[/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]yk=a(xh)^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)