Parabolic Question

Question

During a New Year Celebration, a firework is projected vertically upwards at an angle of inclination and reaches a maximum height of 70m. The firework follows a parabolic path landing 21m from where it was launched. Determine the equation which perfectly describes the parabolic path assuming that the firework was launched at the origin. How high is the firework after travelling a horizontal distance of 7m?

Answer 1

Since a parabola is symmetric around the vertex the x coordinate of the vertex is midway between 0 and 21 which is 10.5 The y coordinate of the vertex is at the max height or 70 so can put the equation in vertex form

y= a(x-10.5)^2 +70

Can use the point (21,0) to solve for a

0= a(21-10.5)^2 +70

-70 = a(10.5)^2

a= (-70)/(10.5)^2

a= -.635 so equation is

7=-.635(x-10.5)^2 +70