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

2024
Views:

285

Pages:

2
Author:

omiliar74be

Module 4 Test Review Name Date KEY Class 1. Cara and Ellen both take a walk through the park. Cara follows a path modeled by the equation y = x + 3. Ellen's path can be modeled by y=(x-3)²+8. Determine if each of the following is a point where the paths will cross. Choose Yes or No. 5. Which statement about a parabola is not true? A. The focus of the parabola lies on the axis of symmetry. Tal x+3=-(x-3)+8 B. The directrix of the parabola is parallel to the axis of symmetry. X+3=(x²-6x118 A. (4.7) X+3=-x+x-948 B. (2.5) x+3=-x²+6x- -x-3 C. (3,6) • Yes O No o Yes No O Yes No -x²+5x-4=0 D. (1,4) Yes No x²-5x+4=0 C. Each point on the parabola is equidistant from the directrix and the focus. Tme 6. Which line intersects the parabola shown below in exactly two points? (x-4)(x-1) x=1 y=1+3=4 2. What is the equation of a parabola with a vertex at (0, 0), a focus at (5, 0), and a directrix x = -57 (y-0)=4(5)(x^o) y² = 20x 3. What is the equation of the parabola with the focus (-2, 4) and the directrix x=27 (y-4)=4(-2)(x-0) (4-4)=-8x 4. Find the missing characteristics of the parabola from the given information. Focus: (0,7) directrix: y = -7 Vertex: (0,0) Opens: up p: 7 Equation: (X-0=4(7) (4-0) x2=28y C A. x=-2 B. y=x+2 (C) y=-x-2 7. Find the equation of the parabola with the focus (-2, 2) and the directrix y = 6. √(-2,4) (x+2)²=4(-2) (y-4) (x+y)=-8(y-4) 8. Solve the system: x^2 + y = 16 y + x = 4 x^2 + 4 - x = 16 x^2 - x - 12 = 0 (x - 4)(x + 3) = 0 x = 4, x = -3 y = 4 - 4 = 0 y = 4 - (-3) = 7 (4, 0), (-3, 7) 9. Solve the system: 8x + y^2 = 12 x + y = 3 x = 3 - y 8(3 - y) + y^2 = 12 24 - 8y + y^2 = 12 y^2 - 8y + 12 = 0 (y - 6)(y - 2) = 0 y = 6, y = 2 x = 3 - 6 = -3 x = 3 - 2 = 1 (-3, 6), (1, 2) 10. Choose True or False for each statement about the parabola with the equation `y^2 - 12x - 2y = 23`. y^2 - 2y + 1 = 12x + 23 + 1 (y - 1)^2 = 12(x + 2) A. The vertex is (1, -2). **False** B. The focus is (1, 1). **True** C. The directrix is x = -5. **True** D. The parabola opens to the left. **True** 11. Determine if each line intersects the parabola shown below in exactly two points. Choose Yes or No. [Image of a parabola and several lines] A. y = 2 **Yes** B. x = 2 **Yes** C. y = -2 **Yes** D. x + y = 2 **Yes** E. x + y = -2 **Yes** 12. The equation for the cross section of a parabolic telescope mirror is `34y = x^2`, measured in centimeters. How far is the focus from the vertex of the cross section? 4p/4 = 34/4 p = 8.5 Since p measures the distance from the vertex to the focus, the focus is 8.5 cm away from the vertex.