Quickly determine the equation of the tangent line to a parabolic curve using our online calculator. Simply input the parabola's coefficients and the x-coordinate of the tangency point to get the slope and full equation (y=mx+b). Master calculus concepts and verify your answers instantly!
Formula:
The general equation of a parabola is given by y = ax2 + bx + c.
To find the tangent line at a point (x0, y0):
- Calculate y0:
y0 = ax02 + bx0 + c - Find the derivative (slope function):
m(x) = dy/dx = 2ax + b - Calculate the slope at x0:
m = 2ax0 + b - Use the point-slope form:
y - y0 = m(x - x0) - Convert to slope-intercept form:
y = mx - mx0 + y0
Variables:
a: Coefficient of x2 in the parabola equation.b: Coefficient of x in the parabola equation.c: Constant term in the parabola equation.x0: The x-coordinate of the point of tangency on the parabola.