VIEWS: 16 PAGES: 7 POSTED ON: 3/28/2012 Public Domain
Solving and Graphing Quadratic Equations 1). Solve 2x² = 10. Then find the x-intercepts of f(x) = 2x² - 10. 2). Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function. f(x) = 2x² - 12x + 23 What is the vertex? What is the line of symmetry? What is the maximum or minimum value? Is the value f(3) = 5 a minimum or maximum? Graph the function. 3). The length of a rectangle is twice the width. The area is 98 yd². Find the length and the width. What is the length? What is the width? 4). Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function. f(x) = x² - 2x – 6 What is the vertex? What is the line of symmetry? What is the minimum or maximum value? Is the value of f(1) = -7 minimum or maximum? Graph the function. 5). The number of tickets sold each day for an upcoming performance of Handel’s Messiah is given by N(x) = -0.5x² + 14x + 11, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day? How many days after the concert announcement will ticket sales peak? How many tickets will be sold on that day? 6). Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the function. f(x) = -(x+9)² - 5 What is the vertex? What is the line of symmetry? What is the maximum or minimum value? Is the value of f(-9) = -5 minimum or maximum? Graph the function. 7). Find the x-intercepts and y-intercepts. f(x) = -x² + 5x + 14 What are the x-coordinates of the intercepts? x = ? The y-intercept is (0,?)? 8). Solve, if possible, for x. x² + 10 = 2x 9). Find the vertex, find the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function. f(x) = 2x² - 12x + 2 What is the vertex? What is the line of symmetry? What is the minimum or maximum value? Is the value, f(3) = -16 minimum or maximum? Graph the function. 10). For the scatterplot, determine which of the following types of functions might be used as a model for the data. a). linear b). quadratic c). not linear or quadratic 11). Solve 6x + x(x-4) = 0. Then, find the x-intercepts of f(x) = 6x + x(x- 4). 12). Determine the nature of the solutions of the equation. x² - 12x + 36 = 0 Choose one: a). two real solutions b). one real solution c). two non-real solutions 13). Solve the formula for the given variable. Assume all variables represent nonnegative numbers. A = 10s², for s. 14). Determine the nature of the solutions of the equation. x² - x + 10 = 0 Choose one: a). one real solution b). two real solutions c). two non-real solutions 15). Give exact and approximate solutions to three decimal places. (x-2)² = 36 16). Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the function. What is the vertex? What is the line of symmetry? What is the maximum or minimum value? Is the value of f(-9) = 4 minimum or maximum? Graph the function. 17). Find and label the vertex and the line of symmetry. Graph the function. f(x) = 2(x-1)² What is the vertex? What is the equation of the line of symmetry? Graph the function. 18). Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax² + bx + c = 0. Solution: 4, only solution What is the equation? 19). Give exact and approximate solutions to three decimal places. x² - 7x + 11 = 0 The exact solutions are x = ? The approximate solutions to 3 decimal places are x = ? 20). Find and label the vertex and the line of symmetry. Graph the function. f(x) = 1/5x² What is the vertex? What is the equation of the line of symmetry? Graph the function. 21). A student opens a mathematics book to two facing pages. The product of the page number is 1332. Find the page numbers. The first page is what? The second page is what? 22). Solve by completing the square. x² + 4x – 45 = 0 23). Give exact and approximate solutions to three decimal places. y² - 20y + 100 = 9