Читать книгу Algebra II: 1001 Practice Problems For Dummies (+ Free Online Practice) - Mary Jane Sterling, Mary Sterling Jane - Страница 13

Chapter 6

Quadratic Functions and Relations

A quadratic function is created from a quadratic expression — an expression with a variable raised to the second power. The graphs of quadratic functions look like U-shaped curves that open upward or downward. A quadratic relation may open left or right. The key to graphing a quadratic function or relation is to find its vertex, determine which way it opens, and find a point or two that can be used to sketch the curve.

The Problems You’ll Work On

In this chapter, you’ll work with quadratic curves in the following ways:

 Determining the vertex and intercepts from the function rule

 Rewriting quadratic functions in the standard form for a parabola

 Sketching the graphs of parabolas

 Using quadratic functions and their properties to solve applications

What to Watch Out For

Don’t let common mistakes trip you up; watch for the following when working with quadratic curves:

 Finding the opposite of the coefficient of b when solving for the coordinates of the vertex

 Watching for the correct direction of the parabola’s opening when sketching

 Performing completing the square correctly when rewriting the parabola’s equation in standard form

 Using the correct property of a parabola when solving an application

Determining the Vertex and Intercepts of a Parabola

301–310 Find the intercept(s) and vertex of the parabola.

301.

302.

303.

304.

305.

306.

307.

308.

309.

310.

Writing Equations of Parabolas in a Standard Form

311–320 Write the equation of the parabola in the standard form . Then identify the vertex.

311.

312.

313.

314.

315.

316.

317.

318.

319.

320.

Sketching Graphs of Parabolas

321–330 Sketch the graph of the parabola.

321.

322.

323.

324.

325.

326.

327.

328.

329.

330.

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)?