Ineed with these other quadratic story problems.

1. 2.12 seconds

2. 10 feet

Step-by-step explanation:

1. "Pekka tosses a ball out of a window that is 40 feet in the air.  Its initial velocity is 15 feet per second.  The path of the ball is represented by:

h = -16t² + 15t + 40

How long does it take for the ball to hit the ground (in seconds) rounded to the nearest hundredth?"

When the ball hits the ground, its height is 0:

0 = -16t² + 15t + 40

0 = 16t² − 15t − 40

Solve with quadratic formula:

t = [ -b ± √(b² − 4ac) ] / 2a

t = [ 15 ± √(225 + 2560) ] / 32

t ≈ 2.12 or -1.18

t must be positive, so t = 2.12 seconds.

2. "Tricia bounces a ball in front of her feet.  The path of the ball from the time it hits the ground until it lands on the floor is represented by:

f(x) = -2(x − 3)² + 10

Assuming that Tricia's feet are located at the origin (0, 0), what is the maximum height of the ball (in feet)?"

The function is a parabola.  The vertex of this parabola is at (3, 10).  So the maximum height is 10 feet.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be