# Quadratics Standard Form

### By: Vikash Singh

## Standard Form Equation:

*y=ax^2+bx+c*

## Learning Goals:

**I learned to use the**

*1*.*Quadratic Formula*to find the

*x-intercepts.*

* 2.* I learned how to use the

*Discriminant*to find how many x-intercepts a quadratic function has.

* 3.* I learned how to graph a

*Quadratic Function*using the

*Quadratic Formula.*

* 4. *I learned how to

*Complete The Square*to find the

*Maximum/Minimum value*of the quadratic and its' vertex.

## Summary:

- Standard for Equation: y=ax^2+bx+c.
- 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.
- MAX or MIN? Complete the square to get vertex form.
- Discriminant Formula: x=(b^2 - 4ac).
- In order to find the x-intercepts use the Quadratic Formula.

## Quadratic Formula:

## Completing The Squares:

- Transforms a standard equation into vertex form to get the vertex and the maximum/minimum value.

## The Discriminant:

- The discriminant Formula is used to identify the number of c-intercepts in a quadratic function
- Given that a,b and c are rational numbers, they are needed to determine the discriminant.
- Discriminant equation: x=(b^2-4ac)

## Here Is a Video to Help You Understand Further How to Complete the Square:

## Standard Form Example:

## Here is an Example of Completing The Square:

## Reflection:

- Quadratics has been a very interesting and fun unit to learn this year. Quadratics compares to many things needed to be done throughout the world.
- During this unit I have made some mistakes, but i practiced and will keep practicing to get better. I was able to succeed and understand the whole unit and apply each of the concepts of the quadratics unit.

## Some Formulas in Quadratics:

## Connections:

**Vertex Form to Graphing:**

- When you have the vertex form of an equation, you are able to identify the vertex and plot the graph.
- When you have plotted the vertex you can you can use the step pattern to get both sides.

**Vertex Form to Standard Form:**

- You must expand vertex form in order to achieve the standard form.
- you can also complete the square from standard form to get to vertex form,

**Standard Form to Graphing:**

- In standard form the c value gives you the y intercept.
- Transform your standard form equation to vertex form by completing the square, and that will give you the vertex.
- Plot the vertex and use the vertex as well as the step pattern to plot your quadratic.

**Factored Form to Graphing:**

- When an equation is in factored Form you can easily find the x-intercepts and the a value.
- You can use the x-intercepts to find the vertex.
- Then plot all points and continue to graph.

**Factored to Standard Form:**

- In factored Form once the two x-intercepts are found by factoring, find the vertex by using AOS, and subbing x into the original equation for y.
- In standard form once the two x intercepts are found, find the vertex by using AOS, and subbing x into the original equation for y.

**All Forms Connecting Together. (Vertex, Standard, Factored)**

- To find the y-intercept for all of these forms, when x=0 the y-intercept is able to be found.
- The y intercept is written as (0,y)

## Assessment: Standard Form Unit Test

- This assessment strengthened my understanding that their are multiple ways to come to a solution.
- I made sure that i was always right by checking my work by completing the square to achieve the vertex of the equation.
- For the vertex, i did it b using the quadratic formula to find the x-intercepts then go along to find the vertex.
- This helped me to realize there are man ways to solve problems.

## This Video Shows the Introduction into Standard Form from Linear Equations:

## Key Terms:

1__.Minimum:__ the lowest point on a parabola that opens up

2.__Maximum__: the highest point on a parabola that opens down

3.__the x-part of the vertex:__ -b/2a

4.__parabola:__ the graph of a quadratic function

5.__standard form of a parabola__: y=ax^2 + bx + c

6.__axis of symmetry:__ the line of reflection for a parabola

7__.y-intercept: __the point where the graph intersects the y-axis

8.__x-intercepts:__ the point where the graph intersects the x-axis

9.__Discriminant: __determines how many solutions a quadratic function has and what kind of number they are.

10.__When discriminant is negative:__ 2 complex imaginary solutions

11.__When discriminant is zero:__ 1 real rational solution

12__.When discriminant is positive:__ 2 real solutions