Determine the maximum yvalue of the function Let a quadratic

Determine the maximum y-value of the function. Let a quadratic function y = 2x^2 + 3x - 5. Find the vertex of the parabola. Sketch the parabola. Find the axis of symmetry of the graph. Find the x and y intercepts of the graph. Find the domain and the range of the function. A baseball is thrown straight up from the rooftop 448feet high.. The function s(t) = -16t^2 + 48 t + 448 describes the ball\'s height above the ground, s(t), in feet, t seconds after it is thrown. How long will it take for the ball to have the maximum height? What is its maximum height? How long will it take for the ball to hit the ground?

Solution

s(t) = -16t^2 + 48t + 448

maximum height : quadratic function has maxima at vertex:

x = -b/2a .So, t = -b/2a =-(48)/(2*-16)

t = 6/4 = 3/2 seconds

It will take 3/2 = 1.5 seconds for the baseball to reach maximum height

Maximum height - Plug t = 3/2 in S(t)

S(1.5) = -16(1.5)^2 + 48*1.5 +448

= 484 feet

When ball hits the ground S(t) =0

-16t^2 + 48t + 448 =0

solve for t : -t^2 + 3t +28 =0

t^2 - 3t -28 =0

t^2 - 7t +4t-28 =0

t(t-7)+4(t-7) =0

(t +4)(t -7) =0

t =-4 ; t = 7 sec

So, t = 7secons base ball reaches ground