Solve for y
y=4\left(x-1\right)^{2}+3
Solve for x (complex solution)
x=-\frac{\sqrt{y-3}}{2}+1
x=\frac{\sqrt{y-3}}{2}+1
Solve for x
x=-\frac{\sqrt{y-3}}{2}+1
x=\frac{\sqrt{y-3}}{2}+1\text{, }y\geq 3
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y-3=4\left(x^{2}-2x+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.
y-3=4x^{2}-8x+4
Use the distributive property to multiply 4 by x^{2}-2x+1.
y=4x^{2}-8x+4+3
Add 3 to both sides.
y=4x^{2}-8x+7
Add 4 and 3 to get 7.
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