628175 Solving and Graphing Quadratic Equations by cGYCwrJ

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									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

								
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