Graphing Quadratic Equations in Standard Form

1. Alain throws a stone off a bridge into a river below.

The stone's height (in meters above the water), $x$ seconds after Alain threw it, is modeled by:

$h(x)=-5 x^{2}+10 x+15$

What is the height of the stone at the time it is thrown?

2. Marquise has $200$ meters of fencing to build a rectangular garden.

The garden's area (in square meters) as a function of the garden's width $x$ (in meters) is modeled by:

$A(x)=-x^{2}+100 x$

What side width will produce the maximum garden area?

3.A certain company's main source of income is selling cloth bracelets.

The company's annual profit (in thousands of dollars) as a function of the price of a bracelet (in dollars) is modeled by:

$P(x)=-2 x^{2}+16 x-24$

What is the maximum profit that the company can earn?

4.Antoine stands on a balcony and throws a ball to his dog, who is at ground level.

The ball's height (in meters above the ground), $x$ seconds after Antoine threw it, is modeled by:

$h(x)=-2 x^{2}+4 x+16$

How many seconds after being thrown will the ball hit the ground?