Respuesta :
Answer:
Vertex: (2, -25); Intercepts: x = -3, 7
Step-by-step explanation:
[tex]y = x^2 - 4x - 21[/tex]
Lets find out the vertex and the x intercepts
To find out the vertex we use formula
[tex]x=\frac{-b}{2a}[/tex]
The value of a= 1, b=-4. Plug in the values
[tex]x=\frac{-(-4)}{2(1)=2}[/tex]
Substitute x=2 and find out y
[tex]y = 2^2 - 4(2) - 21=-25[/tex]
So vertex (2,-25)
Now we find out x intercepts, replace y with 0 and solve for x
[tex]0 = x^2 - 4x - 21[/tex]
we find out two factors whose product -21 and add upto -4
the factors are -7 and 3
[tex]0 = (x-7)(x+3)[/tex]
[tex]x-7=0, x=7[/tex]
[tex]x+3=0, x=-3[/tex]
x intercepts are -3,7
