The Geometry of the Coefficients of a Quadratic Function
Explore the geometric meaning of the coefficients of a quadratic function written in standard form .
Practice Zone
In the app above, set . The parabola now passes through What is the slope of the tangent line at ? Compare your result with the value of the coefficient . What do you notice?
Now set . What is the y-intercept of the parabola? Compare your result with the value of the coefficient (explore different values for ). What is the equation of the tangent line at the y-intercept? What is the slope of the tangent line? What do you notice?