# Quadratic Relationships

### Graphing Vertex Form

## Learning Goals

- Understand how to graph a parabola using an equation
- How to graph using transformation
- Label parts of a parabola
- Different ways to graph a parabola
- How to find the value of (a), (h) and (k) in an equation

Definitions:

Parabola- A two-dimensional, symmetrical curve, that is often shown on a graph

Vertex Form- An equation that uses values of a, h and k to determine the vertex and plot the x and y-intercepts

## Summary

- Vertex (h,k): Axis of symmetry (x=h) and Optimal value (y=k)
- (a) tells you the direction of opening and compression or stretch (in front of the equation)
- (h) horizontal translation (inside the bracket before it is closed)
- (k) vertical translation (the final value at the end of the equation)
- step pattern (a multiplied by 1, 3 and 5)
- to find the y-intercept, set x=0 and solve for y
- to solve, set y=0 and solve for x or expand and simplify to get the standard form, then use the quadratic formula

## Graph

## Parabola in Vertex Form

- y = (x - h)^2 + k form
- Positive Parabola (value of a is positive)
- 3 units to the right (h value is -3 which becomes positive)
- 2 units high (k value is 2)
- Vertex is (h, k)

Vertex Form word problem

Graphing Using Transformations