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[tex]y=ax^2+bx+c[/tex]
c)
[tex]y=2(x-3)^2+1\\\\y=2(x^2-2\cdot x\cdot3+3^2)+1\\\\y=2(x^2-6x+9)+1\\\\y=2\cdot x^2-2\cdot6x+2\cdot9+1\\\\y=2x^2-12x+18+1\\\\\huge\boxed{y=2x^2-12x+19}[/tex]
d)
[tex]y=-3(x+2)^2-4\\\\y=-3(x^2+2\cdot x\cdot2+2^2)-4\\\\y=-3(x^2+4x+4)-4\\\\y=-3\cdot x^2-3\cdot4x-3\cdot4-4\\\\y=-3x^2-12x-12-4\\\\\huge\boxed{y=-3x^2-12x-16}[/tex]
e)
[tex]y=-\frac{1}{2}(x-2)^2+2\\\\y=-\frac{1}{2}(x^2-2\cdot x\cdot2+2^2)+2\\\\y=-\frac{1}{2}(x^2-4x+4)+2\\\\y=-\frac{1}{2}\cdot x^2-\frac{1}{2}\cdot(-4x)-\frac{1}{2}\cdot4+2\\\\y=-\frac{1}{2}x^2+2x-2+2\\\\\huge\boxed{y=-\frac{1}{2}x^2+2x}[/tex]
f)
[tex]y=-\frac{1}{3}(x-3)^2+4\\\\y=-\frac{1}{3}(x^2-2\cdot x\cdot3+3^2)+4\\\\y=-\frac{1}{3}(x^2-6x+9)+4\\\\y=-\frac{1}{3}\cdot x^2-\frac{1}{3}\cdot(-6x)-\frac{1}{3}\cdot9+4\\\\y=-\frac{1}{3}x^2+2x-3+4\\\\\huge\boxed{y=-\frac{1}{3}x^2+2x+1}[/tex]
