Algebra II: 1001 Practice Problems For Dummies (+ Free Online Practice). Mary Jane Sterling

Sketching Graphs of Parabolas

       321–330 Sketch the graph of the parabola.

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Using Quadratic Equations in Applications

       331–340 Solve the following quadratic applications.

      331. The height of a rocket (in feet), t seconds after being shot upward in the air, is given by . How high does the rocket rise before returning to the ground?

      332. The height of a rocket (in feet), t seconds after being shot upward in the air, is given by . How long does it take before hitting the ground?

      333. The height of a ball, t seconds after being shot upward in the air, is given by . How high does the ball get before returning to the ground?

334. The height of a ball, t seconds after being shot upward in the air, is given by . How long does it take before hitting the ground?

      335. The amount of profit (in dollars) made when x items are sold is determined with the profit function . How many items must be sold before the “profit” is positive?

      336. The amount of profit (in dollars) made when x items are sold is determined with the profit function . What is the greatest possible profit?

      337. The average number of skis per day sold at a sports store during the month of January is projected to be , where n corresponds to the day of the month. On what day is the greatest number of skis expected to be sold?

      338. The average number of skis per day sold at a sports store during the month of January is projected to be , where n corresponds to the day of the month. When will the least number of skis be sold?

      339. The average amount of time (in seconds) it takes a person to complete an obstacle course depends on the person’s age. If the function represents the amount of time, in seconds, that a person at age g takes to complete this obstacle course, then at what age is a person expected to be the fastest (take the least amount of time)?

      340. The average amount of time (in seconds) it takes a person to complete an obstacle course depends on the person’s age. If the function represents the amount of time, in seconds, that a person at age g takes to complete the obstacle course, then how much faster is a 20-year-old than a 10-year-old (how many minutes fewer)?

Chapter 7

      Polynomial Functions and Equations

      A polynomial function is one in which the coefficients are all real numbers and the exponents on the variables are all whole numbers. A polynomial whose greatest power is 2 is called a quadratic polynomial; if the highest power is 3, then it’s called a cubic polynomial. A highest power of 4 earns the name quartic (not to be confused with quadratic), and a highest power of 5 is called quintic. There are more names for higher powers, but the usual practice is just to refer to the power rather than to try to come up with the Latin or Greek prefix.

The Problems You’ll Work On

      In this chapter, you’ll work with polynomial functions and equations in the following ways:

       Determining the x and y intercepts from the function rule (equation)

       Solving polynomial equations using grouping

       Applying the rational root theorem to find roots

       Using Descartes’ rule of sign to count possible real roots

       Making use of synthetic division

       Graphing polynomial functions

What to Watch Out For

      Don’t let common mistakes trip you up; watch for the following ones when working with polynomial functions and equations:

       Forgetting to change the signs in the factored form when identifying x-intercepts

       Making errors when simplifying the terms in f(–x) applying Descartes’ rule of sign

       Not changing the sign of the divisor when using synthetic division

       Not distinguishing between curves that cross from those that just touch the x-axis at an intercept

       Graphing the incorrect end-behavior on the right and left of the graphs