Answer:
A. x-intercepts: (4,0),(-2,0)
C. Vertex: (1,-9)
Step-by-step explanation:
We have been given factored form of a quadratic equation
. We are asked to find vertex and x-intercepts of our given equation.
We know that x-intercepts of a graph are those points at which graph touches or crosses x-axis and y-coordinates of x-intercepts are always zero.
So we will substitute
in our given equation to find the x-intercepts.
![0=(x-4)(x+2)](https://tex.z-dn.net/?f=0%3D%28x-4%29%28x%2B2%29)
![(x-4)=0\text{ or }(x+2)=0](https://tex.z-dn.net/?f=%28x-4%29%3D0%5Ctext%7B%20or%20%7D%28x%2B2%29%3D0)
![x-4+4=0+4\text{ or }x+2-2=0-2](https://tex.z-dn.net/?f=x-4%2B4%3D0%2B4%5Ctext%7B%20or%20%7Dx%2B2-2%3D0-2)
![x=4\text{ or }x=-2](https://tex.z-dn.net/?f=x%3D4%5Ctext%7B%20or%20%7Dx%3D-2)
Since y-coordinates of x-intercepts will be 0, therefore, x-intercepts of the graph will be (4,0), (-2,0) and option A is the correct choice.
To find the vertex of the parabola, we will expand our given expression using FOIL.
![(x-4)(x+2)](https://tex.z-dn.net/?f=%28x-4%29%28x%2B2%29)
![x*x+x*2-4*x-4*2](https://tex.z-dn.net/?f=x%2Ax%2Bx%2A2-4%2Ax-4%2A2)
![x^2+2x-4x-8](https://tex.z-dn.net/?f=x%5E2%2B2x-4x-8)
![x^2-2x-8](https://tex.z-dn.net/?f=x%5E2-2x-8)
We will use formula
to find the x-coordinate of vertex of parabola, where, a and b represents the coefficient of
respectively.
![\text{x-coordinate of vertex}=\frac{-(-2)}{2*1}](https://tex.z-dn.net/?f=%5Ctext%7Bx-coordinate%20of%20vertex%7D%3D%5Cfrac%7B-%28-2%29%7D%7B2%2A1%7D)
![\text{x-coordinate of vertex}=\frac{2}{2}=1](https://tex.z-dn.net/?f=%5Ctext%7Bx-coordinate%20of%20vertex%7D%3D%5Cfrac%7B2%7D%7B2%7D%3D1)
Now we will substitute
in the expression to find the y-coordinate of parabola.
![\text{y-coordinate of vertex}=1^2-2*1-8](https://tex.z-dn.net/?f=%5Ctext%7By-coordinate%20of%20vertex%7D%3D1%5E2-2%2A1-8)
![\text{y-coordinate of vertex}=1-2-8](https://tex.z-dn.net/?f=%5Ctext%7By-coordinate%20of%20vertex%7D%3D1-2-8)
![\text{y-coordinate of vertex}=-9](https://tex.z-dn.net/?f=%5Ctext%7By-coordinate%20of%20vertex%7D%3D-9)
Therefore, the vertex of parabola will be at point (1,-9) and option C is the correct choice.