# STANDARD FORM

## LEARNING GOALS

• Understand the process of completing the square
• know how to find the x-intercepts using the quadratic formula
• Graphing using the quadratic formula
• know how to solve all types of word problems

## Completing The square

The process of completing the square involves changing the first two terms of a quadratic relation of the form of y=ax^2 + bx + c into a perfect square while maintaining the balance of the original relation.

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

Ex 1:

y= x^2 + 8x + 5

= (x^2 = 8x) + 5 (b/2)^2 = (8/2)^2

= (x^2 + 8x + 16 - 16) + 5

= (x^2 + 8x + 16) + 5 - 16

= (x + 4) ^2 - 11

vertex: (-4, -11)

Ex 2:

y=2x^2 + 12x + 11

= 2(x^2 + 6x) + 11

= 2( x^2 + 6x + 9 - 9) + 11

= 2(x^2 + 6x + 9) +11 -18

= 2(x+3)^2 - 7

Therefore,the vertex is (-3,-7) and the minimum value is -7

## DISCRIMINANT

D<0 = the equation will have zero solutions

D>0 = the equation will have two solutions

D=0 = the equation will have one solutons

## REFLECTION

Quadratics has taught me a lot of things relating to math and has made my life a whole lot easier. From mapping notation to different types of word problems, quadratics has made my math life a breeze. For example using the mapping notation in the first quadratics unit has helped me graph and find the x- intercepts. I enjoyed using that method in particular because it consumed less of my time and I was very comfortable using it. The unit that stood out the most was the standard form unit because I understood it and it was very easy to get familiar with. If someone was to look at my website for any of the units they would have no problem understanding it and would actually like doing some of the problems. Also in quadratics there is a lot of mix and match. For example, we can take a quadratic equation in standard form and make it factored and find the x- intercepts through that. All of the units relate back to graphing a parabola and have their own ways to finding the necessary information we require to graph the parabola.