Graphing Quadratic Equations in Vertex Form

As you have seen, all parabolas have a vertex and an axis of symmetry. You can write a quadratic equation in vertex form, making it easy to find the vertex and graph. Watch this lecture series and complete the interactive exercises.

Quadratic word problems (vertex form) - Questions

1. A hovercraft takes off from a platform.

Its height (in meters), $x$ seconds after takeoff, is modeled by:

$h(x)=-3(x-3)^{2}+108$

What is the height of the hovercraft at the time of takeoff?

2.A certain company's main source of income is selling socks.

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

$P(x)=-3(x-5)^{2}+12$

What sock price should the company set to earn a maximum profit?

3.The fish population in a certain part of the ocean (in thousands of fish) as a function of the water's temperature (in degrees Celsius) is modeled by:

$P(x)=-2(x-9)^{2}+200$

What is the maximum number of fish?

4. The power generated by an electrical circuit (in watts) as a function of its current $c$ (in amperes) is modeled by:

$P(c)=-20(c-3)^{2}+180$

Which currents will produce no power (i.e. 000 watts)?
Enter the lower current first.

Lower current: ______ amperes

Higher current: ______ amperes