Answer:
Vertex (1,-25), Intercepts at (6,0) and (-4,0)
Step-by-step explanation:
Axis of symmetry = -b/2a = -(-2)/2(1) = 2/2 = 1 so x=1 is the equation of line
Plug x=1 into equation y=1-2-24=-25
factor for x-intercepts: (x-6)(x+4)
set them equal to zero: x-6=0 so x=6 x+4=0 so x= - 4
Answer:
The vertex of the provided equation (1,-25)
The x intercepts are (-4,0) and (6,0).
Step-by-step explanation:
Consider the provided equation.
[tex]y=x^2-2x-24[/tex]
Substitute y=0 to find x intercepts.
[tex]x^2-2x-24=0[/tex]
The above equation can be written as:
[tex]x^2+4x-6x-24=0[/tex]
[tex]x(x+4)-6(x+4)=0[/tex]
[tex](x+4)(x-6)=0[/tex]
By zero product rule:If ab=0 then either a=0 or b=0
[tex]x+4=0[/tex] or [tex]x-6=0[/tex]
[tex]x=-4[/tex] or [tex]x=6[/tex]
Hence, the x intercepts are (-4,0) and (6,0).
If the equation is in the standard form [tex]y=a^2+bx+c[/tex] then the expression [tex]\frac{-b}{2a}[/tex] gives the x coordinate of the vertex.
By comparing the provided equation with standard form we can concluded that: a=1, b=-2 and c=-24
Substitute the respective values in the expression [tex]\frac{-b}{2a}[/tex] we get x coordinates of the vertex:
[tex]\frac{-(-2)}{2(1)}=\frac{2}{2}=1[/tex]
Hence, the value of x=1.
Now substitute the value of x in the provided equation to find the value of y.
[tex]y=(1)^2-2(1)-24[/tex]
[tex]y=1-2-24[/tex]
[tex]y=-25[/tex]
Hence, the vertex of the provided equation (1,-25)
