# Learning Standard Form

### By: Shawn Mangat | Date: 05/06/2016

## Learning Goals

- Learn About The Standard Form Equation
- Learn How To Complete The Squares (Convert Standard to Vertex)
- Learn About The Quadratic Formula
- Learn About The Discriminant
- Learn How To Graph The Equation
- Learn How To Solve Word Problems

## Standard Form Equation

**y=ax^2+bx+c.**

Standard form is the expansion of a factored or vertex form equation.

The value of "a" gives you the shape and direction of opening.

The value of "c" is the y-intercept.

Solve using the quadratic formula, to get the x-intercepts.

Solve using completing the squares to get vertex.

MAX or MIN

In order to determine whether a quadratic equation has a max or min you must first check to see if the "a" value is positive or negative.

If the "a" value is positive you have a min.

If the "a" value is negative you have a max.

In order to determine the max or min coordinates of a standard form equation you must use completing the squares (convert to vertex form) and then determine the vertex.

## Completing The Square

**y=ax^2+bx+c--->y=a(x-h)^2+k**

When completing the square, you are converting a standard form equation to a vertex form equation.

This makes graphing a parabola easier.

- To complete the square, you must factor the first 2 terms of a standard form equation.
- Then you must divide the 'b' value by 2, then square that value.
- Make sure that the value that you get is positive and negative.
- Take the negative value out of the brackets, then multiply it with the 'a' value that we factored the first 2 terms of a standard form equation with.
- Add or subtract the terms that are outside of the brackets.
- Square root the first and the last values that are inside that bracket.
- Put the numbers that are square rooted in a bracket without the squares, make sure that the bracket is squared.
- Also make sure you take the 'b' values operation is in middle of the squared bracket of your final answer.

__Ex:__

y=2x^2-24x-5

y=2(x^2-12x)-5

y=2(x^2-12x+36-36)-5

y=2(x^2-12x+36)-36*2-5

y=2(x^2-12x+36)-72-5

y=2(x-6)^2-77

*Remember in order to convert it back into standard form all you have to do is follow BEDMAS*

## Quadratic Formula

The formula solves for the x-intercepts of a quadratic equation.

In order to use it all you have to do is get a quadratic equation in standard form and then get the a,b & c values.

Once you have the values, you have to input them into the equation and then solve in BEDMAS order.

*Remember ± means that you have to split the equation into 2; one which adds and another which subtracts (replacing the ±)*

## Discriminant

Discriminant formula: **D=b^2-4ac**

If the value of the discriminant is positive and greater than 0, the parabola will have 2 x-intercepts.

If the value of the discriminant is negative, the parabola will have no x-intercepts.

If the discriminant has a value of 0, the parabola will have 1 x-intercept.

In the image to the right the discriminant is 9, which is above 0, so there are 2 x-intercepts.