Parabola and Line Intersection Calculator

Find Intersection Points: Parabola & Line with Step-by-Step Solutions

Solve the system of equations to find where a parabola and a line meet. Complete step-by-step explanation shown for every calculation.

Formula & method

\[ \text{Parabola: } y = a x^2 + b x + c \qquad \text{Line: } y = m x + B \]

Substituting gives the quadratic equation: \( a x^2 + (b - m) x + (c - B) = 0 \)

The discriminant determines if there are 2, 1 (tangent), or 0 intersection points.

Enter coefficients

\(a\) (parabola)

\(b\) (parabola)

\(c\) (parabola)

\(m\) (slope of line)

\(B\) (y-intercept of line)

Decimal places

Intersection Points

Enter coefficients and press "Find Intersection (Show Steps)"

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📐 Step-by-step solution will appear here after calculation.