The quadratic formula
This Grade 6 algebra skill from Yoshiwara Elementary Algebra introduces the quadratic formula as a method for solving any quadratic equation of the form ax^2 + bx + c = 0. The formula x = (-b plus or minus sqrt(b^2 - 4ac)) divided by (2a) gives the solutions directly from the coefficients.
Key Concepts
Property The solutions of the equation.
$$ax^2 + bx + c = 0, \quad a \neq 0$$.
are given by the formula.
Common Questions
What is the quadratic formula?
The quadratic formula is x = (-b plus or minus sqrt(b^2 - 4ac)) divided by (2a). It solves any quadratic equation ax^2 + bx + c = 0 for the variable x.
When should you use the quadratic formula?
Use the quadratic formula when a quadratic equation cannot be easily factored. It always works regardless of whether the equation factors nicely.
What is the discriminant in the quadratic formula?
The discriminant is b^2 - 4ac. If it is positive, there are two real solutions. If zero, one repeated solution. If negative, no real solutions.
How do you identify a, b, and c in a quadratic equation?
In ax^2 + bx + c = 0, a is the coefficient of x^2, b is the coefficient of x, and c is the constant term. Make sure the equation is in standard form first.
Where is the quadratic formula introduced?
The quadratic formula is introduced in the Yoshiwara Elementary Algebra textbook for Grade 6.