# Quadratics

### Standard Form

## Summary of standard form.

__a__** **value tells us the direction of opening.__ __If **a **value is negative parabola opens downwards and if a is positive parabola opens upwards.

Quadratic formula ( in the following picture )

Completing the square help us to find Vertex and change standard to vertex form.

Today I show you the basics of Standard form like How to convert standard to vertex form.

## Standard form

y = ax² + bx + c

## What does a tells us about.

__a__tells you the direction of opening. If a value is negative parabola opens downwards and if a is positive parabola opens upwards.

## How to find Vertex by using completing the square and; convert standard to vertex form.

y = (3x² + 6x) - 10

y = 3(x² + 2x) - 10 { Take out 3 }

y = 3(x² + 2x +1 -1) - 10 { When you divide 2/2 and then square you get 1}

y = 3(x² +2x +1) -3 -10 {Multiply 3 by -1 you get -3 and take it out }

y = 3(x² +2x +1) - 13

y = (x + 1)² - 13 { Now this is vertex form so the vertex is ( - 13, -1)

AND YOU ALSO SEE HERE HOW WE CONVERT STANDARD FORM TO VERTEX FORM.

## Quadratic formula Example to find x intecepts.

## Discriminant

**The discriminant tells us how many solutions (x-intercepts) a parabola will have.**

**D=b^2-4(a)(c)**

**a=2**

**b=6**

**c=12**

D=b^2-4(a)(c)

D=6^2 - 4(2)(12)

D=36-96

__D= -60__

__So, __If the 'D' value is less than '0', than there will be no x-intercepts.

If the 'D' value is '0' than there will be 1 x-intercept.

If the 'D' value is greater than '0', than there will be 2 x-intercepts.

## Video for word problem ; how to solve by completing the square and as well as about revenue.

## Word problem about how to find Rectangle dimensions.

## Word problem about consecutive integers.

## Learning goals

2. Today I also learn about completing the square.