Accepted Answer
Answer:Q1. [tex]f(x) = 4x^{2} -16x+21[/tex] [tex]=4(x^{2} -4x)+21\\\\=4[(x-2)^{2} -2^{2}] +21\\\\=4(x-2)^{2} - 4+21\\\\= 4(x-2)^{2} +17\\[/tex]Q2. [tex]f(x) = -x^{2} -6x-9\\[/tex] [tex]=x^{2} +6x+9\\\\=[(x+3)^{2}-3^{2}] +9\\\\= (x+3)^{2} -9+9\\\\= (x+3)^{2}[/tex]Q3. [tex]y=\frac{1}{2}x^{2} -x+1[/tex] [tex]=\frac{1}{2} (x^{2} -2x)+1\\\\= \frac{1}{2} [(x-1)^{2} - 1^{2}] +1\\\\= \frac{1}{2} (x-1)^{2} -1+1\\\\= \frac{1}{2}(x-1)^{2}[/tex]
Suggested Answer
The answers are in the pic below.