Question

F(x-2)=4x^2+5x-9.

Please explain thoroughly with work. Thank you!

Answer 1

Hello,
If you want f(x) read this.

Explanation:

I am going to use Horner's method.

`\begin {array}c&x^2&x&1\\---&--&--&--\\&4&5&-9\\x=2&&8&26\\---&--&--&--\\&4&13&\boxed{17}\\x=2&&8&42\\---&--&--&--\\&4&\boxed{21}&59\\x=2&&8\\---&--&--&--\\&\boxed{4}&29\\\end {array}\\\\\\F(x-2)=4(x-2)^2+21(x-2)+17\\\\So\ \boxed{F(x)=4x^2+21x+17}\\\\Proof:\\\\F(x-2)=4(x-2)^2+21(x-2)+17\\\\\\=4x^2-16x+16+21x-42+17\\\\=4x^2+5x-9\\`

I hope this is what you want.