Can you run through the quadratic equation(including the sketch and algebra).

A quadratic equation of the form ax^2+bx+c can be solved by factorizing the quadratic equation but before that you must check that b^2-4ac>0 so that the solution is in real numbers and not in complex numbers; in this case b^2-4ac<0. You then find the solutions using the quadratic formula. A more simpler way where factorizing the quadratic equation may also result in the solution which can be used to find the intersection points of the parabola i.e. x^2+2x-3=0 has roots (x+3)(x-1) which tells us that the parabola intersects the x-axis at x=-3 and x=1. The coordinates are (-3,0) and (1,0). Now if you need to know how the parabola looks then if a>0(for the quadratic ax^2+bx+c) then the parabola is happy faced and if a<0 then the parabola is sad faced. To find the minimum or maximum of the parabola all you have to is differentiate it and set it equal to zero because the slope of the tangent to the parabola is flat at min or max. This will give you the x value of the min or max and then you have to substitute it back into the quadratic equation to find the y-value. The parabola ax^2+bx+c also tells us that the y-intersection point is c which is because f(0)=a(0)^2+b(0)+c=c. I can delve further into the topic including all the reasoning for where the quadratic formula comes from and polynomial division but this is a simplified overview of the topic.