Hi, My name is Glenn and i am a student at secondary school. My problem is this; One boundary of a pond is parabolic in shape. The boundary passes through the points A(-20,45), B(40,40) and E(30,35). The equation of the parabola is of the form y=ax2+bx+c. Find the equation of the parabola and the coordinates of the vertex of the parabola. Any assistance you could provide would be greatly appreciated. Thanks Glenn Hi Glenn, Since the equation is of the form y = ax2 + bx + c and A(-20,45) is on the graph you know that 45 = a (-20)2 + b 20 + c thus 400 a + 20 b + c = 45 Use the points B and C to obtain two more linear equations in the variables a, b and c. Solve these equations for a, b and c. Penny /* This script is written by Eric (Webcrawl@usa.net) For full source code, installation instructions, 100's more DHTML scripts, and Terms Of Use, visit dynamicdrive.com */ function printit(){ if (window.print) { window.print() ; } else { var WebBrowser = '<OBJECT ID="WebBrowser1" WIDTH=0 HEIGHT=0 CLASSID="CLSID:8856F961-340A-11D0-A96B-00C04FD705A2"></OBJECT>'; document.body.insertAdjacentHTML('beforeEnd', WebBrowser); WebBrowser1.ExecWB(6, 2);//Use a 1 vs. a 2 for a prompting dialog box WebBrowser1.outerHTML = ""; } } var NS = (navigator.appName == "Netscape"); var VERSION = parseInt(navigator.appVersion); if (VERSION > 3) { document.write('<form><input type=button value="Print this Page" name="Print" onClick="printit()"></form>'); } * Registered trade mark of Imperial Oil Limited. Used under license.

Hi,
My name is Glenn and i am a student at secondary school. My problem is this;
One boundary of a pond is parabolic in shape. The boundary passes through the points A(-20,45), B(40,40) and E(30,35). The equation of the parabola is of the form y=ax²+bx+c. Find the equation of the parabola and the coordinates of the vertex of the parabola. Any assistance you could provide would be greatly appreciated.
Thanks Glenn

Hi Glenn,

Since the equation is of the form y = ax² + bx + c and A(-20,45) is on the graph you know that

45 = a (-20)² + b 20 + c

thus

400 a + 20 b + c = 45

Use the points B and C to obtain two more linear equations in the variables a, b and c. Solve these equations for a, b and c.

Penny