Question

Does anyone, know how to do this???

Answer 1

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}

Step-by-step 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}