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Algebra 1

9.11.3 Comparing Maximums between Quadratics

Algebra 19.11.3 Comparing Maximums between Quadratics

9.11.3 Comparing Maximums between Quadratics

9.11.3 • Comparing Maximums between Quadratics

Activity

A function AA, defined by p(600−75p)p(600−75p), describes the revenue collected from the sales of tickets for Performance A, a musical.

The graph represents a function BB that models the revenue collected from the sales of tickets for Performance B, a Shakespearean comedy.

In both functions, pp represents the price of one ticket, and both revenues and prices are measured in dollars.

1.

Without creating a graph of AA, determine which performance gives the greater maximum revenue when tickets are pp dollars each. Explain or show your reasoning.

Video: Comparing Maximums between Quadratics

Watch the following video to learn more about comparing maximums between quadratics.

Comparing Maximums between Quadratics

Self Check

A function, defined by p(600−60p)p(600−60p), describes the revenue collected from the sales of tickets for a concert where pp is the price of one ticket. Find the maximum revenue, in dollars.

  1. 1500
  2. 10
  3. 5
  4. 600

Additional Resources

Finding Maximum Revenue

The revenue brought in by a newspaper is modeled by R=p(−2500p+159,000)R=p(−2500p+159,000). Find the maximum revenue where RR is revenue and pp is price per newspaper subscription.

Step 1 - Find the horizontal intercepts or xx-intercepts (where p=0p=0).

First intercept -

This occurs at p=0p=0 or (0,0)(0,0).

Second intercept -

−2500p+159,000=0−2500p=−159,000p=63.6−2500p+159,000=0−2500p=−159,000p=63.6

Step 2 - Find the xx-coordinate of the vertex halfway through the horizontal intercepts.

The vertex (of a graph) will occur halfway between p=0p=0 and p=63.6p=63.6. This occurs when p=31.8p=31.8.

Step 3 - Write in the function in standard form and substitute p=31.8p=31.8.

R=−2500p2+159,000pR=−2500p2+159,000p

R=−2500(31.8)2+159,000(31.8)R=−2500(31.8)2+159,000(31.8)

The maximum revenue is at $2,528,100 with a $31.80 subscription.

Try it

Finding Maximum Revenue

Suppose that the price per unit in dollars of a cell phone production is modeled by p=$45−0.0125xp=$45−0.0125x, where xx is in thousands of phones produced, and the revenue represented by thousands of dollars is R=x·pR=x·p. Find the production level that will maximize revenue and the maximum revenue.

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