# Vertex Form

## LEARNING GOALS

• We can use the 1st and 2nd differences from a data table to determine if a equation is linear, quadratic or neither.
• We can use a table of values to create a parabola
• We can graph a basic quadratic equation without using technology

## How Can You Tell If A Line Is Linear or Non-Linear (Quadratic) ?

Well....

Linear Relationships: Points that follow a straight line are known as linear relationships.

Here are examples you can try to guess...

## Something Called The Mapping Formula ?!

The general mapping rule for quadratics is

(x,y) → (x + h, ay + k)

The variables a, h and k can be found in the turning point formula: y = a(x - h)² + k

Example: y=4x2+16

To get y = 4x² + 16 to turning point formula, you must complete the square

y = 4x² + 16

Divide each side by 4 to get rid of any factors before x²

y/4 = x² + 4

y/4 = (x + 0)² - 0 + 4

y = 4(x + 0)² + 16

Therefore: a = 4, h = 0, k = 16

Substitute these values into (x,y) → (x + h, ay + k)

(x,y) → (x + 0, 4y + 16)

Therefore: (x,y) → (x, 4y + 16)

## How To Write Quadratic Equations Given The Vertex And A Point

Just as quadratic equations can map a parobla, the parobla points can help write a corresponding quadratic equation. In vertex form, y=a(x-h)^2+k, the variables h and k are coordinats for the parobla's vertex. The x point sign much change though.

First substitute the vertex's coordinates for h and k in the vertex form equation. For example let use a vertex of (2,3). The equation would be y=a(x-2)^2+3.

Then substitute the point's coordinate for x and y in th equation. In this case w can use points (3,8). The new equation would be 8=a(3-2)^2+3.

After solve the equation for a. In this example solving for a would result in a becoming 5.

Lastly subsitute the values of a into the first equation. The final answer should be y=5(x-2)^2+3.

## Finally An Easy Way Out Graphing by Using The Step Method !

Graphing By Using the Step Method

## Word Problems In Vertex Form

Word problems in vertex form are simple application problems given that the equation already provides information on how to solve it. Vertex form questions are usually solved using the vertex. Factored form and vertex form are alike as the methods to solve them are similar. After solving a vertex form word problem it is concluded with a defined variable or “Let” statement, work shown, solved answers and "Therefore" statement concluding your determined problem.