need help please! would love to know how to solve this problem

Question

What are the equations of two lines that pass through the point (-1,-3) and are tangent to the graph of y=x^2+ 1

Answer 1

y^' = 2x = m_tan

y + 3 = 2x(x + 1)

y = 2x² + 2x - 3. But this equation of the tangent line must also satisfy the original equation so ...

2x² + 2x - 3 = x² + 1

x² + 2x - 4 = 0

by quad formula: x = (-2 ±√20)/2 = -1 ±√5

So y = (-1 + √5)(x +1) - 3. and y = (-1 - √5)(x +1) - 3