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


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.