# Standard Form

## Learning Goals for unit

• Use the Quadratic equation to find x-intercepts of standard for equations
• Complete the square to convert standard form into vertex for and find the vertex of a parabola

## Standard Form: y= ax^2 + bx + c

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

The value of c is coordinate

The value of b can translate into the x coordinate

## Quadratic formula: Finding x intercepts

The quadratic formula is by completing the square for ax^2+bx+c=0 and solving for x.

It is a direct way of the roots. And knowing all this information it can help create a graph.

It is used when an equation cannot be factored

## The discriminant formula is d= b^2-4a

The discriminant is the name given to the expression that appears under the square root sign in the quadratic formula. The discriminant tells you about the "nature" of the roots of a quadratic equation given that a, b and c are rational numbers.

## Maximum or Minimum Values: Completing the square

Completing the square is a way to take an equation and make it so it can be able to be put into the vertex form. Also using this method it will help you find the vertex of the parabola.
IMG 3837
IMG 3840

## Word Problems

x= 2 √-2² -4(3)(-65)

2(3)

x= 2√784

6

x=2 (+-) 28

6

x = 30/6 x=5 x = -26/6 x= -4.333 (Not valid)

Therefore x is 5 feet and the dimensions are 5 feet and 13 feet.

5*13 = 65

## Reflection

The quadratic unit was relatively easy, which is why I am disappointed with the marks I got on most tests. concepts like factoring were confusing at the beginning and increasingly became easier to understand and carry out. The things that we learned in unit

1,

and 2 of quadratics had major roles in the last part of the unit. We learned

graphing

, vertexes, and x- intercepts in the first part. In the third we worked towards finding them using two different ways, quadratic formula and completing the square.

its

very important to follow the formulas very precisely or you'll risk messing up 1 part and getting the wrong answer to the whole equation. This happened to me many times.

we learned multiples ways to graph a parabola which all involved finding x-intercepts in some way and then find the vertex of the parabola which became easy with practice and paying attention to the finer details.

After thoroughly practicing and understanding the topics and techniques I was able to prove it with better results.