¿dentro del origen?

¿será parábola con vértice en origen?

¿has buscado en Internet?

f(x) = ax² + bx + c ← this is a parabola

y = mx + b ← this is a line

Point of intersection between the parabola and the line: f(x) = y

ax² + bx + c = mx + b

ax² + bx + c - mx - b = 0

ax² + x.(b - m) + (c - b) = 0

Δ = (b - m)² - 4a.(c - b)

Δ < 0 → no solution → no point

Δ = 0 → only one solution → no point

x = - (b - m)/2a

x = (m - b)/2a

Δ > 0 → two solutions → 2 points

x₁ = [- (b - m) + √Δ]/2a = (m - b + √Δ)/2a

y₁ = mx₁ + b

x₂ = [- (b - m) - √Δ]/2a = (m - b - √Δ)/2a

y₂ = mx₂ + b