IXL - Solve quadratic equations: word problems (Precalculus practice)

Emma built a model rocket as a summer project. After she launches the rocket, it soars up into the sky. It runs out of fuel at a height of 450 feet when it is traveling upward at a velocity of 100 feet per second. The rocket continues upward for a time and then falls back down to the ground.

Which equation can you use to find how many seconds it takes the rocket to hit the ground after running out of fuel?

If an object travels upward with an initial velocity of

feet per second from

feet above the ground, the object's height in feet,

after

seconds can be modeled by the formula

–

450

100

–

100

450

To the nearest tenth of a second, how long does it take the rocket to hit the ground after running out of fuel?

seconds

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Learn with an example

question

Bob's band, Laser Trio, booked a venue to perform next weekend. They want to know how much to charge per ticket to make $700 in revenue, since that's how much they just spent on a new drum set. Based on past performances, the expression

–

135

can be used to predict the number of tickets the band will sell based on the ticket price,

Which equation can the band use to estimate the ticket price that will make them $700 in revenue?

700

(

–

135

)

700

(

–

135

)

What two ticket prices will make the band exactly $700 in revenue?

solution

To find the ticket prices, first write an equation. Revenue, or the total amount of money the band will make, is equal to the ticket price times the number of tickets they sell.

revenue

ticket price

number of tickets

You want to know when the band will make $700 in revenue, and the expression

–

135

can be used to predict the number of tickets the band will sell. The ticket price,

is the variable.

700

(

–

135

)

Now, solve for

Start by writing the equation in standard form.

700

(

–

135

)

700

–

135

–

135

–

700

To solve for

you can use the quadratic formula with

–

135

and

–

700

–

(

135

)

(

135

)

–

(

–

)

(

–

700

)

(

–

)

–

135

4,225

–

135

–

135

–

or p

–

135

–

7 or p

So, the band will make exactly $700 in revenue if the ticket price is $7 or

$20.

Looking for more? Try this:

$Confetti$

Excellent!

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Teacher tools

Work it out

Not feeling ready yet? These can help:

D.8Solve a quadratic equation using the quadratic formula

D.6Solve a quadratic equation by factoring

Z.1Solve a quadratic equation using square roots

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