Explore the geometric meaning of the coefficients of a quadratic function written in standard form [math]y=ax^2+bx+c[/math].
In the app above, set [math]c=0[/math]. The parabola now passes through [math]C=\left(0,0\right)[/math][br]What is the slope of the tangent line at [math]x=x\left(C\right)[/math]?[br]Compare your result with the value of the coefficient [math]b[/math].[br]What do you notice?
Now set [math]b=0[/math]. What is the [i]y[/i]-intercept of the parabola?[br]Compare your result with the value of the coefficient [math]c[/math] (explore different values for [math]c[/math]).[br]What is the equation of the tangent line at the [i]y[/i]-intercept?[br]What is the slope of the tangent line?[br]What do you notice?[br]