University:
College Entrance Preparation
Course:
ACT Preparation (Mathematics)
Academic year:

2022
Views:

295

Pages:

11
Author:

pravitate8aj11

1. MODELING WITH MATHEMATICS The table shows the speeds of a car as it travels through an intersection with a stop sigu. What type of function can you use to model the data? Estimate the speed of the car when it Semester 1 Review is 20 yards past the intersection. Absolute Value Smith Displacement from sign (yards), x Speed (miles per hour), y -100 40 -50 20 -10 4 0 0 10 4 50 20 100 40 2. PROBLEM SOLVING You are playing basketball with your friends. The height (in feet) of the ball above the ground 1 seconds after a shot is released from your hand is modeled by the function f(t)-16+321 + 5.2. a. Without graphing, identify the type of function that models the height of the basketball. Quadratic h. What is the value of / when the ball is released from your hand? Explain your reasoning. Os e. How many feet above the ground is the ball when it is released from your hand? Explain. 5.247 3. Write a function g whose graph represents the indicated transformation of graph f. f(x)=-2x-41+2 21 (4, 1) (4, 2) 4 2 966)=-18-4/+1 5. ABSTRACT REASONING If and y have a positive correlation, and y and have a negative correlation, then what can you conclude about the correlation between x and z? Explain. It is negative 4. MODELING WITH MATHEMATICS The data pairs (x, y) represent the average annual tuition y (in dollars) for public colleges in the United States years after 2005. Use the linear regression feature on a graphing calculator to find an equation of the line of best fit. Estimate the average annual tuition in 2020. Interpret the slope and y-intercept in this situation. (0, 11.386), (1, 11.731), (2, 11,848) (3, 12,375), (4, 12,804), (5, 13,297) Y = 380 x + 11,290; $16,990 Tuition increases $380 each your Cost of tuition in tous is then 11,290 6. Solve the following system: x+3y-z-2 x+y-2=(0 As x inertises, y morerses, s. 2. de crears.3.x + 2y-32-1 7. Write a rule for g described by the transformations of the graph of f. Then identify the vertex. 1 fix)(x+6) +3: horizontal shrink by a factor of and a translation I unit down, followed by a reflection in the 1-axis g(x)=(2x+12)²-2 (-6,-2) (2-1,1,2) 8. Find the minimum or maximum value of the function. Describe the domain and range of the function, and where the function is increasing and decreasing. f(x)=-2x²+8x+7 Max value is 15 D: R R: Y≤ 15 The funchn is thereesing to the left of x=2 and decreasing & the right of k=2 9. PROBLEM SOLVING A woodland jumping mouse hops along a parabolic path given by y=-0.2+1.3x, where x is the mouse's horizontal distance traveled (in feet) and y is the corresponding height (in feet). Can the mouse jump over a fence that is 3 feet high? Justify your answer. No, Vetex is (3.25, 2.1125) 10. Use the Distance Formula to write an equation of the parabola. (Section 2.3) Ay F(0, 1) P(x, y) X D(x,-1) y 1 2 Not drawn to scale 11. Identify the focus, directrix, and axis of symmetry of the parabola. Graph the equation. b. 6x2+3y=0 focus (-5,0) Directrix is x5 AS x-axis focus: (08) Directrix: y=18 As y-axis 12. Identify the vertex, focus, directrix, and axis of symmetry of the parabola. Describe the transformations of the graph of the standard equation with p 1 and vertex (0, 0). (y-3)2+1 16 I unit right, 3up Vertex (1,3) focus (513) my As yo b. y=-x+2)² + 1 Veriut (-2,1) 2 units left, In't focus (-2,0) up. Directrix 2 13. Write an equation of the parabola shown. vertex AY directrix AS X-2 14. Write an equation of the parabola shown. AY 3 2 focus vertex 1 Y=x²+1 2x 15. PROBLEM SOLVING The latus rection of a parabola is the line segment that is parallel to the directrix, passes through the focus, and has endpoints that lie on the parabola. Find the length of the latus rectum of the parabola shown. 16. Write equation of the parabola in standard form: a. That passes through (0, -24) and has vertex (-6,-12) y=(x+c)2-12 b. That has x-intercepts of-16 and -2; passes through (-18, 72) y= 2.25 (x+1)(x+2) c. passes through (-2, 7), (1, 10), and (2, 27) latus rectum AY F(0, 2) V(0, 0) A 68 B 2