Answer to Question #144177 in Algebra for sage

Question

LaToya throws a ball from the top of a bridge. Her throw is modeled by the equation y=-.5x^2+3x+12 and the bridge is modeled by the equation y=-.2x+9. About how far does the ball travel horizontally before its first​ bounce?

Answer 1

$y_1=-5x^2+3x+12$,

$y_2=-2x+9$,

$y_1=y_2$,

$5x^2-5x-3=0$,

$x_1=\frac{1-\sqrt{\frac{17}{5}}}{2}$ ,

$x_2=\frac{1+\sqrt{\frac{17}{5}}}{2}$ ,

$x_2-x_1=\sqrt{\frac{17}{5}}\approx1.84.$