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THINGS to KNOW FOR Test on 8.1, 8.2, 8.3, 8.7, 7.3, 6.7 and Open Boxes 1. 8.1 Distance and Midpoint 2. 8.3 Circles: graph, domain, range, tangent to an axis, give equation from graph, give equation from endpoints, give equation from shifting, give equation from center and radius, and give center/radius from an equation in standard form (ax2 + by2 + cx + dy + e = 0) 3. 6.6 and 8.2: Parabolas A. graph, give pertinent information (vertex, axis of symmetry, focus, directrix, domain, range) B. Give equation in vertex form if in standard form; given a vertex & pt; given focus/directrix/vertex 4. 8.7: Solve systems of equations algebraically & graphically; graph inequalities 5. Yellow sheet: Open box problems (find maximum and dimensions if given a formula) 6. 7.3: Solving equations 7. 7.6: Solving polynomial equations by graphingsynthetic substitutionquadratic formula Sample Problems 1. Give the equation of the following parabolas A. Directrix of x=3 and focus (-1,4) B. Vertex of (-2,3) and goes through the point (1,8) C. The Gateway Arch is 630 ft. wide, 630 ft tall and is in the shape of a parabola. Write an equation of the arch. (Let the origin be located at the bottom left of the arch. Also, how high is the arch 10 ft from the bottom left of the arch? 2. Graph the following. Give the domain and range of each. If it’s a circle then give center and radius. If it’s a parabola then give vertex, axis of symmetry, focus, directrix, and opening A. (x – 2)2 + y2 = 48 B. x = 1/4y2 + 2y + 1 C. y = -2x2 – 6x D. x2 + y2 – 2x2 – 11y2 + 6 = 0 E. 2(x – 2) = (y-3)2 3. Give the equation of the circles with the following conditions: A. Center (2,3) and radius 3 5 B. Center (1,-3) and tangent to y-axis C. (x-3)2 + (y+1)2 = 9 and shifted 2 rt, 3up D. Endpoints of diameter are (-1,3) and (-5, -3) 4. Solve the following system of equations algebraically and graphically X2 + y2 = 25 & x + y = 7 5. Graph the following inequalities: x2 + y2 +6x – 8y + 9 < 0 and x > (y + 2)2 – 4 6. An open box is made from a 10 x 12 piece of paper. A. Find the maximum volume B. Find the dimensions that will yield a volume of 48 in2 7. Find the zeros of x4 + x3 – 7x2 – 9x - 18 = f(x)