# Standard Form

### Quadratic Relations

## 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

Solve Quadratic Equations using Quadratic Formula

## Finding solutions for an equation: Discriminant

## 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

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

1,

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

, 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.