Graphing Quadratic Equations in Standard Form

If a quadratic equation is written in standard form, it can be converted to vertex form by using the vertex formula or completing the square. Watch this lecture series and complete the interactive exercises.

Quadratic word problems (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?