# Quadratic Relationships

### Standard Form

## Learning Goals

-Learn how to use the standard form formula to solve problems

-Find a,b and c in the standard form equation

-Use the Quadratic Formula to find x-intercepts

-Find AOS (Axis of Symmetry) to plot the parabola or find the Max or Min

-Change standard form into vertex form by completing the square

## y = ax^2 + bx + c

## Summary

- 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
- Complete the square to get vertex form
- X-intercepts and AOS
- Plug in AOS to find MAX OR MIN

## Quadratic Formula -Plug in a,b and c to find x-intercepts -Find AOS using the intercepts -Solve a word problem | ## Standard Form to Vertex Form -Complete the square and graph the parabola | ## Find A,B and C -Plug in the values into the quadratic formula to find x-intercepts |

## Completing the Square Example

__Equation__: x^2-8x+24=0

__Move 24 to the other side__: x^2-8x=-24

__Divide b/2 then square root__: (-8/2= 4, 4^2= 16) x^2-8x+16=-24+16

__Vertex Form__: (x-4)^2=-8

Solving Quadratic Equations using the Quadratic Formula - Example 1

Completing the Square to Solve Quadratic Equations: More Examples - 1

Example 4: Applying the quadratic formula | Quadratic equations | Algebra I | Khan Academy