# Standard Form

## Learning Goals

• You will be able to change an equation from vertex form to standard form
• You will be able to change a quadratic equation in to vertex form by completing the squares
• You will be able to identify whether to use the quadratic formula or completing the squares in an equation

## Standard Form

The form ax^2+bx+c=0 is known as a standard type of a quadratic equation.

## Maximum And Minimum

The y-coordinate of the parabola's vertex is also the maximum or minimum value of the quadratic function represented by the parabola.

## Completing The Squares

To complete the squares you must first write the equation in standard form y=ax^2+bx+c.

Here are some examples on how to change from vertex form to standard.

3.14 Completing the square

## Completing Squares Simplified Steps

1. Group x-terms.

2. Common factor just the value of “a” from the x-terms. Simply factor out the number in front.

3. Divide the coefficient of the middle term by two, square it, then add and subtract that number inside the brackets.

4. Remove the subtracted term from the brackets. On the way out of the brackets, it is multiplied by the “a” value that you factored out.

5. Write the perfect square trinomial as the square of a binomial

## Steps On How To Solve The Using The Quadratic Formula

1. A standard form, ax^2 + bx + c, determines the values of a, b and c in the quadratic formula.
2. First plug in the values to the quadratic formula and solve using BEDMAS principles.
3. When done square rooting the number, separate the positive and the negative (between -b ± √) off separately to get both of the zeroes/x-intercepts.
4. Solve both branches and you will end up with both your x-intercepts/zeroes.

## Discriminates

The discriminate can be used to determine how many solution an equation will have.

The equation for discriminate is D=b²-4ac and you substitute the values from your original equation to solve for the discriminate. If the discriminate is more than 0 that means that there will be 2 solutions. If the discriminate is 0 then there will be 1 solution and lastly if the discriminate is less than 0 there will be no solutions.

Example:

D=3²-4(2)(-5)

D=9-4(-10)

D=9+40

D=49

This means that there is 2 solutions.

D=2²-4(1)(1)

D=4-4

D=0

This means there is 1 solution

D=2²-4(5)(2)

D=4-4(10)

D=4-40

D=36

This means there are no solutions