Answer:
The x intercepts are x=-4 and x=2
axis of symmetry x=-1
vertex (-1,-9)
D: {x: all real numbers}
R: {y: y≥ -9}
Explanation:
f(x) = x^2+2x-8
y= x^2+2x-8
Factor the equation
What 2 numbers multiply to -8 and add to 2
4*-2 = -8
4+-2 =2
y = (x+4) (x-2)
The x intercepts are found when we set y =0
0= (x+4) (x-2)
Using the zero product property
x+4=0 x-2 =0
x=-4 and x=2
The x intercepts are x=-4 and x=2
The axis of symmetry is halfway between the x intercepts. It is symmetric must be in the middle of the x intercepts
1/2 (-4+2) = 1/2(-2) = -1
The axis of symmetry is at x=-1
To find the vertex, it is along the axis of symmetry. Substitute x=-1 into the equation
y = (x+4) (x-2)
y = (-1+4) (-1-2)
=3*-3
=-9
The vertex is (-1,-9)
The domain is the values that x can take
x can be any number
D: {x: all real numbers}
The range is the values that y can take
since the parabola opens upward, the vertex is the minimum,Y must be greater than or equal to -9
R: {y: y≥ -9}