Solve the questions below and choose the correct answer from the multiple choices:

1) For the following parabola, state the coordinates of the vertex.

12y + x ? 4x= ? 16

For numbers 10-12: Match the equation with the graph. The graphs are on the next page. Try drawing a quick sketch of each before looking at the answer choices. Each choice can be used more than once or not at all. 10) 9x- -36x+4y- +24y+36=0 11) 4x- +16x+9y- -54y+61=0 (x-2)2 () + 3) 2 + =1 12) 4 9\f13. Identify the conic section: 81 4 A) Parabola B) Ellipse C) Hyperbola D) Circle E) None of the above 14. Solve the system of equations: 4x3 +92 =72 4x-3y- =0 A. (-3, 2) and (-3, -2) B. (3, 2) and (3, -2) C. (3, 2). (3,-2), (-6. 2 2 ) and (-6, -2V2) D. (3, 2), (3, -2), (6, 2 2 ) and (6, -212) E. No solution F. None of these15. Graph and solve the system of equations: 1=yz-4y xty=0 A. (-3, 3) and (3, -3) B. (-3, 3) and (0,0) C. (3, -3), (-3,3), (0, 0). (-3,1) D. (3, -3), (-3,3), (0, 0) E. No solution F. None of these16. Graph the parabola x =4y- and the circle x-+ (y+1)- =1. At how many points do these graphs intersect? A. 0 B. 1 C. 2 D. 3 E. 4 F. None of theseProblems 17-20: For each equation, determine which description listed below best describes the graph of the equation. Note: the answer choices given may be used more than once or not at all. A. Ellipse B. Parabola C. Point D. Two intersecting lines E. One line F. No graph 17. x' +5y- =-8 18. x= y -4y+7 19. ( x - 1 ) + ( y -3) =0 20. 4x- -9y= =0\f2. Which of the following equations define a parabola with the given information: Vertex (3,1), opening to the left. A. (x-1)= =-2(y-3) B. (y-1) =2(x-3) C. (y-1) =-8(x-3) D. (y-3) =-4(x-1) E. (x-1)' =2(y-3) F. None of the aboveFor numbers 3-4, match each equation to its graph. 3. y- = -4(x+1) 4. y' =4(x-1) A. B. C. D. E. F. None of these5) Write the equation in standard form: 25x +4y- -100x-8y =-4 (x+ 1) A. + () +2)= =1 B. (x-2)3 + ()-1)' =1 25 25 C. (x-2)2 ()-1)3 (x-2)2 + =1 D. 4 100 + (y-1)= =1 25 (x-2)2 E. (y-1)2 + =1 F. None of the above 100 4A circle is a special case of an ellipse where a=b. It then follows that c'=a'-b'=a'-a'=0,50 0=0. (Therefore, the foci are at the center of the circle, and this is simply labeled as the center and not the focus.) The standard form for the equation of a circle is ( x - h ) + ( y - k ) =p (Note: If each term in the above equation were divided by y , it would look like the standard form for an ellipse, with a =ber .)\fA. (x -5) +(1-5) =1 B. (x - 5)2 +(1-5)2=116 C. (x -5)2 +(1-5) =V116 D. ( x + 2)2 +(1+5)? =29 E. (x - 5) +(1-5) =29+ 4x-14v+50=0\f9) Complete the square and find the vertices of this ellipse: 4x- -16x+9y- -18y =11 A) (5,1), (-1,1) B) (2,3), (2,-1) C) (-2,1), (4,1) D) (2,4). (2,0) E) (-2,2), (4,2) F) None of these