Quadratic Equations Practice Questions PDF

Name: Class: Date: Question #1 The equation below relates two variables. 2 y − 2 = x Which statement BEST describes the relationship between any pair of x- and y‑values that satisfy...

Name: Class: Date: Question #1 The equation below relates two variables. 2 y − 2 = x Which statement BEST describes the relationship between any pair of x- and y‑values that satisfy this equation? A The value of x is less than the square root of y. B The value of x is more than the square root of y. C The value of y is more than the square of x. D The value of y is less than the square of x. Question #2 Consider this quadratic equation. y = a (x − b) (x − c) Which statement about the equation is always true? A b and c determine the roots B b and c determine the minimum C b and c determine the domain D b and c determine the range Question #3 Consider this expression. 2 −2x − 3x + 4 Which statement about this expression is true? A There is a real number that represents the maximum value for the variable x. B There is a real number that represents the minimum value for the variable x. C There is a real number that represents the minimum value of the expression. D There is a real number that represents the maximum value of the expression. Question #4 A f (x) = −x 2 + 8x − 12 B f (x) = x 2 − 8x + 12 C f (x) = (x + 2) (x + 6) D f (x) = (x − 4) 2 + 4 E f (x) = (x − 4) 2 − 4 F f (x) = (x − 2) (x − 6) Question #5 The height in feet of a projectile, y, as a function of x, the time in seconds, is described by this equation. 2 y = −16x + 32x − 24 Rewrite the equation in the form y = a(x − h) + k, where 2 a, h, and k are real numbers. Use the on-screen keyboard to type your answer in the box below. y= Question #6 Jessica was asked to find the minimum value of the quadratic expression 2x 2 − 12x + 17 by completing the square. She used the following steps: 2 2 2 2 Step 1 : 2 (x − 6x ) + 17 Step 2 : 2 (x − 6x + 9 − 9) + 17 Step 3 : 2 (x − 6x + 9) − 9 + 17 Step 4 : 2(x − 3) + 8 Jessica's teacher told her that one of her steps was wrong. Which step is incorrect and why? Step 1 is incorrect because 2 must first be factored out of all three terms in the expression in order to A correctly complete the square. Step 2 is incorrect because the value that needs to be added to complete the square should be −3 B instead of 9. C Step 3 is incorrect because −9 needs to be multiplied by 2 when it is taken out of the parentheses. D Step 4 is incorrect because x 2 − 6x + 9 factors as (x + 3) instead of (x − 3). Question #7 Trevor wants to prove the polynomial identity that begins as (x + a) (x + b). What is the final form of this polynomial after the binomials are multiplied? A 2x + ab B x 2 + ab C x 2 + abx + ab D x 2 + (a + b)x + ab Question #8 A x 2 + 6x + 9 = 0 B x 2 + 6x + 9 = 16 C x 2 + 6x + 9 = 25 D (x + 3) 2 = 0 E 2 (x + 3) = 16 F 2 (x + 3) = 25 Question #9 x= or x = Question #10 Solve each equation by completing the square. x 2 − 12x = −20 x= or x= 9x 2 + 12x + 5 = 10 x= or x Question #11 a. Write and solve an equation to determine the prices at which the theater would earn $1,500 in profit from the comedy show each weekend. $ and $ b. At what price would the theater make the maximum profit? $ c. What is the maximum profit? $ Question #12 [This is the stem.] [ x + 6 = x2 ] Question #13 If f (x) = 4x 2 , what is f ( − 2)? − 3x + 7 A –3 B 5 C 17 D 29 Question #14 A tennis player hits a ball high into the air. The equation below describes how f (x) , the tennis ball's height in feet, depends on x, the time in seconds the ball is in the air. 2 f (x) = −16x + 96x For each of the five values of x below, drag and drop the correct value of f (x). Value of x Value of f (x) 0 1 2 3 4 0 1 2 3 4 64 80 96 128 144 192 Question #15 A quadratic function is defined by g(x)=(x + 4)2. + 7 a. What is the vertex of the graph of function g(x)? b. Does the vertex represent the minimum value or the maximum value of the function? c. If you were to shift this graph 6 units down from where it is now, what would be the equation represented by the new graph?. g(x) = Question #16 A quadratic function is defined by g(x)=(x + 4)2. + 7 a. What is the vertex of the graph of function g(x)? b. Does the vertex represent the minimum value or the maximum value of the function? c. If you were to shift this graph 6 units down from where it is now, what would be the equation represented by the new graph?. g(x) = Question #17 a. What is the vertex of the graph of function g? b. Does the vertex represent the minimum value or the maximum value of the function? c. If you were to shift this graph 6 units down from where it is now, what would be the equation represented by the new graph? Question #18 Mark is graphing a parabola that has an x-intercept of –4 and a y-intercept of 16. Which of the following functions is he graphing? A 2 f (x) = x − 8x + 16 B f (x) = x 2 + x − 4 C f (x) = x 2 + 8x + 16 D f (x) = −4x 2 + 16 Question #19 Which graph represents a quadratic function with a minimum point of (−3,3) ? A B C D Question #20 Which graph best represents the function f (x) = 0.2(x 2 − 4x − 5) ? A B C D Question #21 A scientist is studying the amount of phosphorous in parts per million at different levels of depth in the soil. In the graph, 2 feet under the surface is –2 feet. The function used to model her results is shown in the graph. What is the domain for the function as it relates to the scientist’s study? A −5 ≤ x ≤ 0, x is an integer B −5 ≤ x ≤ 0, x is a real number C 0 ≤ x ≤ 9, x is an integer D 0 ≤ x ≤ 9, x is a real number Question #22 The chief financial officer for an office supply company presents a function to the company president. The function models the number of proposed stores (up to 11) and the projected net profit for the company. The graph for the function is shown. What is the domain of the function? A integer numbers from –1 to 11 B integer numbers from 1 to 11 C real numbers from –1 to 11 D real numbers from 1 to 11 Question #23 A ball is launched upwards with a slingshot from the top of an 80-foot building. The graph below shows the function that models the trajectory of the ball. Use the drop-down menu to select the correct answers to complete the statement. The domain of this function is from only whole numbers only rational numbers all real numbers to. 0 2 5 80 144 0 5 8 144 200 Question #24 A diver jumps into a pool from a board ten feet above the surface of the water. Her height, h, at any time t seconds after jumping is given by the equation h = t − 8t + 10. What is the minimum height that she 2 reaches? (Note: Negative values of h mean the diver is below the water.) A –26 feet B –10 feet C –6 feet D –4 feet Question #25 The height of a batted baseball, in feet, after t seconds is given by h(t) = −16t + 80t + 3. How many 2 seconds does it take for the ball to reach its maximum height after it has been hit? A 1.25 seconds B 2.5 seconds C 5 seconds D 6.25 seconds Question #26 Which graph represents the equation y = x 2 + 4x − 5 ? A B  C D Question #27 What is the equation of the quadratic function that passes through the points (0, −1), (1, 0), and (2, −3) ? A y = −2x 2 + 3x + 1 B y = x 2 − 1 C y = −2x 2 + 3x − 1 D y = −x 2 + 1 Question #28 Which of the following describes a city population that is increasing as a linear function of time? One year, a city population increases by 6,000. The next year, the population increases by 6,500. The A population change continues to increase by 500 each year. B Each year, a city population increases by 1,500. One year, a city population increases by 1,500. In each succeeding year, the population increase is twice C that of the previous year. D Each year, a city population increases by 5%. Question #29 Which table shows a linear relationship between time and length? Time (years) Length (inches) 0 40 1 43 A 2 46 3 49 4 52 5 55 Time (years) Length (inches) 0 40 1 41 B 2 43 3 46 4 50 5 55 Time (years) Length (inches) 0 40 1 41 C 2 43 3 47 4 55 5 71 Time (years) Length (inches) 0 40 1 43 D 2 44 3 47 4 48 5 51 Question #30 A B C D Question #31 What are the zeros of the quadratic function below? 2 f (x) = 3x + 11x − 4 A x = −4 and x = 1 3 B x = 4 and x = 1 3 C x = 4 and x = − 1 3 D x = −4 and x = − 1 3 Question #32 What are the x-intercepts of the graph of this equation? 2 y = 4x − 9 A − 4 9 and 4 9 B − 2 3 and 2 3 C − 3 2 and 3 2 D − 9 4 and 9 4 Question #33 Whose stone hit the water first?. Select 1 for Clare and select 2 for Lin. What was the maximum height of Clare's stone? feet What was the maximum height of Lin's stone? feet Question #34 [This is the stem.] a.Whose stone hit the water first? When did that happen? seconds after the stone was thrown. b.Clare’s stone reached its maximum height 14 seconds after it was tossed. Did Clare’s stone reach a higher maximum than Lin’s stone? c.What was the maximum height of Clare's stone? ft