Answer:
C. x-intercepts: (-4,0), (-2,0)
E. Vertex: (-3,-1)
Step-by-step explanation:
Part 1) Find the x-intercepts
we have
[tex]y=(x+4)(x+2)[/tex]
This is a vertical parabola written in factored form
[tex]y=(x-x_1)(x-x_2)[/tex]
where
x_1 and X_2 are the roots or x-intercepts
so
[tex]x_1=-4\\x_2=-2[/tex]
Remember that the x-intercepts are the values of x when the value of y is equal to zero
therefore
The x-intercepts are
(-4,0) and (-2,0)
Part 2) Find the vertex
we have
[tex]y=(x+4)(x+2)[/tex]
This is a vertical parabola open upward (the leading coefficient is positive)
The vertex is a minimum
Applying distributive property
[tex]y=x^2+2x+4x+8\\y=x^2+6x+8[/tex]
Convert to vertex form
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]y=(x^2+6x+3^2)+8-3^2[/tex]
[tex]y=(x^2+6x+9)-1[/tex]
Rewrite as perfect squares
[tex]y=(x+3)^2-1[/tex] ----> equation in vertex form
[tex]y=(x-h))^2+k[/tex]
where
(h,k) is the vertex
therefore
The vertex is the point (-3,-1)
