1. Parabola, 3, 1, -1: y=2(x+3)-4x+(x-3)(x+1) simplifies to y=x^2-4x+3, and the zeros of the graph of the equation occur when y=0. To solve 0=x2-4x+3, use the factored form 0=(x-3)(x-1) and set each factor equal to zero. Then, solve for x: (x-3)(x-1)=0 (x-3)=0 (x-1)=0 x=3 x=1 The graph of the quadratic equation ax^2+bx+c is a parabola with an axis of symmetry x=-b/2a, and the maximum or minimum value of a parabola lies on the axis of symmetry. Find the equation which represents the axis of symmetry, and find the y-value for the determined value of x: For =x2-4x+3, a=1,b=-4,c=3. The axis of symmetry is x= (-(-4))/2(1) =2. When x=2, y=(2)2-4(2)+3=4-8+3=-1. Practice with the free PARCC practice test on PracticeTestGeeks (1,350+ questions with answer explanations).
2. C, D, E; y=3/2 x+3: The rate of change in a linear relationship is constant. In the given table, the output, or y, value decreases by three as the input, or x, value decreases by 2. The slope m of the line between the two given points is, therefore, (-3)/(-2)=3/2. A linear equation can be written in slope-intercept form, y=mx+b. Substitute one of the given x-y pairs and the determined slope into the equation to find the y-intercept b: y=mx+b 3=3/2(0)+b 3=b Using the determined slope and y-intercept, the equation of the line in slope-intercept form is y=3/2 x+3. Using this equation, input values x=0,4,-2,-5 gives output values y=3,9,0,-4.5, respectively. Of the answer choices, (-2,0),(4,9), and (-5,-4.5) lie on the same line the one which passes through given points (2,6) and (0,3).
The graph as x approaches -2 from the left is linear; the slope of the line is 2, and, if the line were extended, it would cross the y-axis at 4. Therefore, in slope-intercept form, the equation of the line is y=2x+4. The function is defined by this line for all x-values less than or equal to -2. Once x exceeds -2, the graph is a parabola. This parabola is the graph of y=x2 shifted down one unit, so its equation is y=x2-1.
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Try these questions from our free PARCC practice tests. The correct answer and an explanation follow each question.
1. An instrument store gives a 10% discount to all students off the original cost of an instrument. During a back to school sale an additional 15% is taken off the discounted price. Julie, a student at the local high school, purchases a flute for $306. How much did it originally cost?
Answer: C. $400
To find the original cost, we need to reverse the discounts. First, the $306 price represents 85% of the price after the initial 10% discount (100% - 15% = 85%). So, $306 / 0.85 = $360. This $360 then represents 90% of the original cost (100% - 10% = 90%). Therefore, $360 / 0.90 = $400, which is the original cost.
3. A skyscraper is 548 meters high. The building's owners decide to increase its height by 3%. How high would the skyscraper be after the increase?
Answer: D. 564 meters
First, calculate the increase in height by finding 3% of 548 meters: 0.03 * 548 = 16.44 meters. Then, add this increase to the original height of the skyscraper: 548 + 16.44 = 564.44 meters. Rounding to the nearest whole meter, the skyscraper would be 564 meters high.
22. Mrs. Jones was formally head of the history department at Center High School. No error.
Answer: A. A
The word "formally" means in a formal or official manner. However, the sentence intends to convey that Mrs. Jones *previously* held the position. The correct word for "in the past" or "formerly" is "formerly," indicating a past status or role.
12. Many reading lists for high-school students include translations from Scandinavian writers such as Lagerlog, Undset, and Ibsen. No error.
Answer: E. E
The sentence contains no grammatical errors, punctuation mistakes, or issues with word usage. The plural subject "Many reading lists" correctly agrees with the plural verb "include," and all other parts of the sentence are structured properly. Therefore, 'No error' is the correct choice.
Prepare for the PARCC - Partnership for Assessment of Readiness for College and Careers exam with our free practice test modules. Each quiz covers key topics to help you pass on your first try.