Algebra Tutorials!

 Wednesday 18th of January

Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

## Completing the Square

The Vertex Form of a Quadratic Function

The format for a quadratic equation given above,

y = a Â· x 2 + b Â· x + c, where the letter x represents the input, the letter y represents the value of the output and the letters a, b and c are all numbers, is called standard form.

Other ways of writing the equations for quadratic functions include vertex form,

y = a  Â· (x - h) 2 + k,

where the letter x represents the value of the input, the letter y represents the value of the output and the letters a, h and k all represent numbers. Just as in standard form, in vertex form the number a cannot be equal to zero. Converting a quadratic equation to vertex form is often quite helpful as it allows you to determine exactly where the graph of the quadratic equation reaches its â€œlow pointâ€ or â€œhigh pointâ€ very easily. Every single quadratic formula can be converted to vertex form. The process for doing this conversion is called completing the square.

What the Vertex Form of a Quadratic can tell you about the graph

The vertex form of a quadratic function:

y = a  Â· (x - h) 2 + k,

also tells you whether the graph of the quadratic is smiling or frowning. To check, simply look at the value of a, as you would if the equation had been written in standard form. If the value of a is positive then the quadratic is smiling and if the value of a is negative then the quadratic will be frowning.

The vertex form of a quadratic equation can also tell you about the location of the highest point (on a frowning quadratic) or the lowest point (on a smiling quadratic â€“ see Figure 1 on the next page). This point (the highest point on a frowning quadratic or the lowest point on a smiling quadratic) is called the vertex.

The x-coordinate of the vertex is the number h that appears inside the parentheses of the vertex form and the y-coordinate of the vertex is the number k that appears outside the parentheses in the vertex form.

Figure 1: (a) In this quadratic, a = -1 and the shape of the graph is a â€œfrown.â€ The vertex in this case is the highest point on the graph. (b) In this quadratic a = 0.5 and the shape of the graph is a â€œsmile.â€ The vertex in this case is the lowest point on the graph.