•  A quadratic function can be expressed in the form \(f(x)=ax^2+bx+c\), where \(a\), \(b\) and \(c\) are constants and \(a \ne 0\).

• If \(a\gt 0\), graph has the shape \(\LARGE \smile\) which passes through a minimum point.

• If \(a\lt 0\), graph has the shape \(\LARGE \frown\) which passes through a maximum point.

\(b^2-4ac>0\)

\(b^2-4ac=0\)

\(b^2-4ac<0\)

• A quadratic function can be expressed in the form \(f(x)=a(x-h)^2+k\) where \(a\), \(h\) and \(k\) are constants and \(a \neq 0\).
• In this form, \(x=h\) is an axis of symmetry and \((h,k)\) is the coordinate of minimum or maximum point.

• A quadratic function can be expressed in the form \(f(x)=a(x-p)(x-q)\) where \(a\), \(p\) and \(q\) are constants and \(a \neq 0\).
• In this form, the roots of the quadratic function are \(p\) and \(q\).
• The axis of symmetry, \(x=\dfrac{p+q}{2}\).
• The coordinate of minimum or maximum point is \(\left[ \dfrac{p+q}{2}, f \left( \dfrac{p+q}{2} \right) \right]\).

•  A quadratic function can be expressed in the form \(f(x)=ax^2+bx+c\), where \(a\), \(b\) and \(c\) are constants and \(a \ne 0\).

• If \(a\gt 0\), graph has the shape \(\LARGE \smile\) which passes through a minimum point.

• If \(a\lt 0\), graph has the shape \(\LARGE \frown\) which passes through a maximum point.

\(b^2-4ac>0\)

\(b^2-4ac=0\)

\(b^2-4ac<0\)

• A quadratic function can be expressed in the form \(f(x)=a(x-h)^2+k\) where \(a\), \(h\) and \(k\) are constants and \(a \neq 0\).
• In this form, \(x=h\) is an axis of symmetry and \((h,k)\) is the coordinate of minimum or maximum point.

• A quadratic function can be expressed in the form \(f(x)=a(x-p)(x-q)\) where \(a\), \(p\) and \(q\) are constants and \(a \neq 0\).
• In this form, the roots of the quadratic function are \(p\) and \(q\).
• The axis of symmetry, \(x=\dfrac{p+q}{2}\).
• The coordinate of minimum or maximum point is \(\left[ \dfrac{p+q}{2}, f \left( \dfrac{p+q}{2} \right) \right]\).