SOLUTION: Two projectiles are shot into the air from the same location. The paths of the projectiles are parabolas and are given by (a) y = −0.0013x2 + x + 19 and (b) y = -x^2/81 +4/

Question 1146285: Two projectiles are shot into the air from the same location. The paths of the projectiles are parabolas and are given by
(a) y = −0.0013x2 + x + 19 and
(b) y = -x^2/81 +4/3x + 19
where x is the horizontal distance and y is the vertical distance, both in feet. Determine which projectile goes higher by locating the vertex of each parabola. (Round your answers to two decimal places.)
(a) y = −0.0013x2 + x + 19
(x,y)=
(b) y = -x^2/81 +4/3x + 19
(x,y)=
Answer by Shin123(626) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Completing the Square for Quadratics

To complete the square for the quadratic , we must first find a square which when expanded, has -0.0013x² and 1x in it.
Factoring -0.0013 from the left side gives . is the square we are looking for. So we get . Taking the -162544.378698225 out of the -0.0013, we get . Subtracting 211.307692307692 from both sides, we get . Since the right side is negative, there are no real solutions.

(384.62,211.31)

Solved by pluggable solver: Completing the Square for Quadratics

To complete the square for the quadratic , we must first find a square which when expanded, has -0.012345679x² and 1.33333333x in it.
Factoring -0.012345679 from the left side gives . is the square we are looking for. So we get . Taking the -4454.999992791 out of the -0.012345679, we get . Subtracting 54.999999856 from both sides, we get . Since the right side is negative, there are no real solutions.

(54,55). went higher then .
Click here for a link to the solver above.
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