Example: Find the quadratic function that passes through the points (2,17), (6,5), and (8,-10).<\/strong><\/p>\n Solution: We don’t know the vertex, nor two points of the same height, so we imagine our equation is of the form<\/p>\n y=ax2<\/sup>+bx+c<\/p>\n and plug in our known points for x and y.<\/p>\n First, based on (2,17):<\/p>\n a(2)2<\/sup> + b(2) + c = 17 ⇒ 4a+2b+c=17<\/p>\n Next, (6,5):<\/p>\n a(6)2<\/sup> + b(6) + c = 5 ⇒ 36a+6b+c=5<\/p>\n Finally, (8,-10):<\/p>\n a(8)2<\/sup> + b(8) + c = -10 ⇒ 64a+8b+c=-10<\/p>\n So we arrive at the three-variable system<\/p>\n This system can be solved manually, with a spread sheet, or with a calculator. Presently I’m using the Sharp el-520w. I press MODE 2 1 to get into three-variable system mode, then enter the parameters row by row. (See my post here<\/a> for insight.)<\/p>\n The solution: a=-.75, b=3, c=14<\/p>\n Therefore, the quadratic function that contains the points (2,17), (6,5), and (8,-10) is<\/p>\n y=-.75x2<\/sup> + 3x + 14.<\/p>\n HTH:)<\/p>\n Source:<\/p>\n Johnson, Lee W. et al. Introduction to Linear Algebra<\/u>, second ed. Don Mills: Addison-Wesley, 1989.<\/p>\n\n