Answer:
[tex]f(0)=-6\\\\f(2)=26\\\\f(-2)=-6\\\\f(x+1)=4(x+1)^2+8(x+1)-6=4x^2+16x+6\\\\f(-x)=4x^2-8x-6[/tex]
Step-by-step explanation:
[tex]f(x)=4x^2+8x-6\\------------------\\f(0)\to\text{put x = 0 to the equation of the function}\ f(x):\\\\f(0)=4(0)^2+8(0)-6=0+0-6=-6\\----------------------\\f(2)\to\text{put x = 2 to the equation of the function}\ f(x):\\\\f(2)=4(2^2)+8(2)-6=4(4)+16-6=16+16-6=26\\-----------------------\\f(-2)\to\text{put x = -2 to the equation of the function}\ f(x):\\\\f(-2)=4(-2)^2+8(-2)-6=4(4)-16-6=16-16-6=-6\\------------------------[/tex]
[tex]f(x+1)\to\text{substitute instead of x expression (x + 1)}\\\\f(x+1)=4(x+1)^2+8(x+1)-6\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\ \text{and the distributive property}\\\\f(x+1)=4(x^2+2x+1)+8x+8-6=4x^2+8x+4+8x+8-6\\\\\text{combine like terms}\\\\f(x+1)=4x^2+(8x+8x)+(4+8-6)=4x^2+16x+6\\-----------------------[/tex]
[tex]f(-x)\to\text{substitute instead of x expression (-x)}\\\\f(-x)=4(-x)^2+8(-x)-6=4x^2-8x-6[/tex]
