PARCC High School Algebra 1 Practice Test Questions
1. Fill in the blanks to complete the following sentence. The graph of the equation y=2(x+3)-4x+(x-3)(x+1) is a __________ with zeros at ___ and ____ and a minimum at y=___.
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.
2. Part A: If there exists a linear relationship between the input and output values, which, if any, of these input/output pairs can be included in the data set? Choose all that apply.
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).
3. The solution to which of the following systems of inequalities is graphed below?
4. Simplify the expression.
5. Write a piece-wise function to describe the graph below.
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.