Solving Quadratic Equations by Factoring

• If the discriminant is positive, there are two real solutions; if it's zero, there is one real solution; if it's negative, there are no real solutions.
• The quadratic formula can be used to find the roots (x-intercepts) of any quadratic equation.
• To solve a quadratic equation using factoring, first identify the leading coefficient and then factor out that term.
• To solve a quadratic equation using factoring, first identify the leading coefficient and factor out that term.
• Next, look for factors that multiply to give the quadratic expression inside the parentheses.
• Finally, set each binomial equal to zero and solve for x.
• When solving quadratic equations with complex roots, use the quadratic formula or complete the square method.
• When solving a quadratic equation with complex roots, use the quadratic formula or complete the square method.
• Finally, set each factor equal to zero and solve for x.
• When solving quadratic equations with complex numbers, use the quadratic formula or complete the square method.
• Quadratic equations have at most two x-intercepts, which correspond to the zeros of the function.
• Quadratic functions have a parabola shape when graphed on a coordinate plane.
• Factoring is useful when solving equations with perfect square trinomials or when finding zeros of functions represented as polynomials.
• When factoring a quadratic function, always check your answer by multiplying the factors together and comparing them to the original polynomial.
• Factored form is useful when finding the zeros of a polynomial.
• The discriminant is b^2 - 4ac.
• The quadratic formula is used when the quadratic equation cannot be solved by factoring.