Quadratic Equations and Quadratic Functions Review

Quadratic Equations ax 2 +bx+c=0 1.Solve by: a.Factoring b.Completing the Square c.The Quadratic formula 2.Find the nature of the roots – Use the discriminant D=b 2 -4ac D>0 means two real roots (if D is perfect square then they are rational) D=0 means one real rational root D<0 means two complex conjugate roots 3.Sum of the roots will be Product of the roots will be 4.To form a quadratic equation if you know the roots use: x 2 – (sum of roots)x + product of roots =0

Quadratic Functions Vertex formGeneral Form Axis of symmetry is x=h Vertex is (h,k) a>0 parabola opens up and has minimum a<0 parabola opens down and has maximum |a|>1 parabola is narrow |a|<1 parabola is wide To find x-intercepts, set f(x)=0 and solve To find y-intercept, set x=0 and find y Axis of symmetry is Vertex is a>0 parabola opens up and has minimum a<0 parabola opens down and has maximum |a|>1 parabola is narrow |a|<1 parabola is wide To find x-intercepts, set f(x)=0 and solve The y intercept is (0,c) When plotting the graph of a quadratic function, find and draw the vertex and axis of symmetry, then plot one other point and the point symmetric to it and always label the scales on both axes.