Three Forms of a Quadratic Function

For a quadratic, a 0. Each form reveals a different graph feature. **Form** | **General equation** | **Feature it reveals** | **Example** Expanded | y=ax2+bx+c | y-intercept at (0,c) | y=x2-2x-3 y-intercept (0,-3) Factorised | y=a(x-p)(x-q) | x-intercepts at x=p and x=q | y=(x+1)(x-3) x=-1, x=3 Completed square | y=a(x-h)2+k | Turning point at (h,k) | y=(x-1)2-4 turning point (1,-4) x2-2x-3=(x+1)(x-3)=(x-1)2-4 Line of symmetry x=- b2a **Form you have** | **Line of symmetry** y=ax2+bx+c | x=- b2a y=a(x-p)(x-q) | x= p+q2 — midway between the x-intercepts y=a(x-h)2+k | x=h Set each factor equal to zero: (x+1)=0 gives x=-1.