UNIT #8 QUADRATIC FUNCTIONS AND THEIR ALGEBRA REVIEW QUESTIONS

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1 Answer Ke Name: Date: UNIT #8 QUADRATIC FUNCTIONS AND THEIR ALGEBRA REVIEW QUESTIONS Part I Questions. For the quadratic function shown below, the coordinates of its verte are, (), 7 6,, 6 The verte is the peak or low point on the quadratic function:, 6. A quadratic function has selected values shown in the table below. If its domain is all real numbers, which of the following represents the range of this quadratic function?, 6 6, () 6,5,6 From the table we can tell this is a quadratic with a minimum (smallest) -value of 6. So the range will be from 6 on up Which of the following quadratic function has a maimum value of 6? () For a quadratic to have a maimum value (instead of a minimum) the leading coefficient must be negative. That is onl true for (). () 4. Which of the following could be the equation of the quadratic shown below? Eplain our reasoning. () Since this is a quadratic function whose that opens upward, a must be positive. Since it has a negative -intercept, c must be negative. The onl quadratic with both of these is.

2 5. The quadratic function f has one zero at 5 other zero? 5 () 5 6. Which of the following is the turning point of the function and a turning point at,. What is the value of its The zeroes of a quadratic will be the same horizontal distance from its turning point. Since 5 is 8 units to the left of, the second zero must be 8 units to the right at. 8? 8, 8, () 8, 8, This quadratic is a shift of 8 units to the right and units down. Hence, its turning point moves from (, ) to (8, -). 5? 7. Which of the following represents the range of the function g () 5 5 This quadratic has a turning point at (-5, ) and opens downward. Thus, its top -value is and then the go down from there. 8. The quadratic function 8 7 can be written equivalentl as () If the quadratic function f is graphed below along with the quadratic function following could be a correct equation for g? 4 9 () g, which of the g () g The function g() has been reflected in the -ais and stretched out. So, it must be choice (). f g g g () emathinstruction, RED HOOK, NY 57, 5

3 . The solutions to the equation 5 are and 5 and 5 () and,, and 5 B the Zero Product Law: or. Which of the following is the solution set to the equation 66? 6,6 8, () 6,6, The solution set to 8 4 is and 4 () and and 4 4 and Which of the following represent the zeroes of the function? and and () 5 and and () 4. Which of the following is the turning point of the function 5?, 6, 7 (), 4, 8 The turning point's -coordinate will be at the midpoint between the two zeroes of and 5. Since these are 8 units apart, the midpoint -value is. Substituting into the equation we find , to the turning point is at, 6. emathinstruction, RED HOOK, NY 57, 5

4 5. The product of two consecutive integers is 4 more than si times the smaller integer. Which of the following equations could be solved to find the smaller integer, n? () n n n4 n 7n4 n 5n4 6n4 6. Which of the following represents the solution set to the equation below? 7 4, 7, () 6,, 8 If we let the smaller integer be n, then the larger integer would be n and our equation would be: nn 6n4 n n 6n4. 6n4 6n4 n 5n Which of the following quadratic has the same zeroes as 7? () Since we can rewrite () as: Its zeroes will still be and. () 8. Which of the following represents the turning point of the quadratic function 5?, 5, () 5,, 74 Use Completing the Square to rewrite: Which of the following represents a correct equation for the parabola shown below? () 5 Since this quadratic function has zeroes at and, it must have factors of and. emathinstruction, RED HOOK, NY 57, 5

5 Free Response Questions. A quadratic function has a turning point at, 8. Selected values for the function are shown in the table below f (a) Finish filling out the table. (b) State the zeroes of the function. A quadratic function has outputs that are smmetric (the same) on either side of its turning point. We use this to fill out the table. The zeroes of the function as the -values where the function's output is zero. The output is zero when and 5.. For the quadratic function (a) Graph the function for the stated domain interval. f 4 defined on the interval f() (b) State the interval over which f is increasing. (c) Is part of an interval where f or f? Eplain our choice. Since f, is part of an interval where f.. Place the quadratic 4 79 into verte form b using the method of completing the square and then state the coordinates of its verte Verte at: 6, 7 emathinstruction, RED HOOK, NY 57, 5

6 . Solve the following equation for all values of Solve the following equation for all values of Three cousins have ages that are consecutive integers. The product of the two older cousin's ages is twelve less than si times the sum of the ounger two cousin's ages. Write an equation that could be solved to find the three cousin's ages. Eplain how our equation models the information provided. n n n n 6 If we let the smallest age be n, then the net two ages are n and n n. Si n. The product of the larger two is then times the sum of the oungest two would be 6n n subtracting, we get twelve less than this sum. and b Find the ages of the three cousins algebraicall. n n n n n n n n n 6 n n n n6 n6 n 9n8 n n 8 n n So the cousins could be:,, and n n 8 So the cousins could be: 8, 9, and emathinstruction, RED HOOK, NY 57, 5

7 6. A rectangle has a length that is nine feet less than four times its width. Its area is 9 square feet. Algebraicall determine the length of its width and length. Show the work that leads to our answer. Let the width be w Then the length will be 9 Area width length w 9 9 w w w w w 9 9 9w w 4 Reject because the value of w cannot be negative. w 6 66 w 6 width 6 feet length feet 7. A rectangular garden originall measured 5 feet b feet as shown below. A path was created around the garden b increasing each side of the original rectangle b -feet on both sides. ft 5 ft Epress the length and width of the larger rectangle in terms of. and 5 If the area of the path that rings the garden is 54 square feet, find the value of Area of Large Rectangle Area of Small Rectangle Area of Path reject emathinstruction, RED HOOK, NY 57, 5 or.5 feet