Answer:
Vertex : (1,-25) ; x intercepts : (6,0)&(-4,0)
Step-by-step explanation:
[tex]y=x^{2}-2x-24[/tex]
adding 25 on both sides
[tex]y+25=x^{2}-2x-24+25[/tex]
[tex]y+25=x^{2}-2x+1[/tex]
[tex]y+25=x^{2}-2*1*1*x+1^{2}[/tex]
[tex]y+25=(x-1)^{2}[/tex]
let us convert the above equation in the standard form
let y+25=Y
x-1=X
[tex]X^{2}=4*\frac{1}{4}*Y[/tex]
vertex of above equation is (0,0)
replacing them into original form is x-1=0 , x=1
y+25=0 ; y=-25
Hence the vertex is (1,-25)
Part 2 :
In order to find the x intercepts , we put y=0 and solve for x
[tex]0+25=(x-1)^{2}[/tex]
[tex]25=(x-1)^{2}[/tex]
taking square roots on both sides we get
±5=x-1
solving get x=±5+1 ; x=5+1=6 ; x=-5+1=-4
Hence y intercepts are (-4,0) & (6,0)
