Completing the Square turns a standard form equation into a Vertex Form Equation. 

 

Steps

1. Remove the Remove the common factor (coefficient) from the "x-squared term" and the "x-term.

2. Find the constant that must be added and subtracted to creat a perfect square. 

*Hint: use this formula- (b divided by 2)^2. 

3. Group the three terms that from the perfect square by moving the subtracted number outside of the bracket by multiply by the common factor first. 

4. Factor the perfect square after collecting like terms. 

 

 

Example

 

 

 

 

 

                                                                                           

 

 

 

 

 

 

 

 

Solving Quadratic Equations using the Quadratic Formula

 

 

 

 

 

 

 

 

 

This formula can be used to solve for all the roots/x-intercepts of a quadratic equation. 

 

Steps

1. Plug in the "a", "b" and "c" values into the equation where indicated. 

2. Solve

 

 

 

Example

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Connection:Once you find your x-intercepts/zeros, you can find your axis of symmetry (by adding the zeros, then                     divinding them by 2). After this, you can use your axis of symmetry to find the y-intercept/ the y value.                     Now you would have both zeros and your vertex

 

 

Discriminant

 

 

The number inside the square root (formula above)  of the quadratic equation is called the Discriminant (D). It helps us determine how many solutions a quadratic eqation has.

 

Steps

1. Plug in the "a", "b" and "c" values.

2. Solve

 

Possibilities:

- If there is a negative number there is no solution to this equation

- If there is a positive number there are two solutions to this eqaution.

- If the value is a 0 after solving thre is one solution.  

 

Example of each possibility: