# Quadratics

### Graphing Vertex Form

## Index

Image of Graph

Find x and y intercepts

Find Equation

Videos for Graph Quadratic Function in Vertex form

Video for Graphing with transformations

Word problem

Learning Goals

## Summary of Vertex form

**Vertex form = a(x − h)² + k**

**Vertex (h,k)**

**Axis of symmetry (x=h)**

**Optimal value y=k**

** a **tells you the direction of opening as well as compression or stretch

__h__ tells you horizontal translation

__k __tells you vertical translation

Step pattern : **Starting from the vertex as "the first point" ... **

OVER 1 (right or left) from the vertex point, UP 1² = 1 from the vertex point

OVER 2 (right or left) from the vertex point, UP 2² = 4 from the vertex point

OVER 3 (right or left) from the vertex point, UP 3² = 9 from the vertex point

OVER 1 (right or left) from the vertex point, UP 1² = 1 from the vertex point

OVER 2 (right or left) from the vertex point, UP 2² = 4 from the vertex point

OVER 3 (right or left) from the vertex point, UP 3² = 9 from the vertex point

## Axis of Symmetry

## Optimal value

## What does a tells you about?

**a**value is negative parabola opens downwards and if

**a**is positive parabola opens upwards.

**a**also help you to find points with step pattern.

## How to find vertex?

Vertex is (-4,-6) because +4 is h and it is changed into -4, K is -6 so this is the vertex (-4,-6).

## The following image is of graph. You see which thing graph where.

## How to find y-intercept if x set to 0.

**Example: y=-1(x-3)²+4**

**y = -1(0-3)²+4(put x=0 in this equation).**

**=-1(-3)²+4**

**=-1*9+4**

**=-1*13**

**y=-13 **

## To solve for x, set y=0.

y = a(x − h)² + k

**Example: y= 2(x-4)²-50**

**0=2(x-4)²-50**

**0-50=2(x-4)²**

**50/2=2(x-4)²/2**

**√25=√(x-4)² [square root both side]**

**5=x-4**

**5+4=x**

**x=9**

## How to find an equation?

y = a(x − h)² + k

y=a(x+3)²-4 ------------** I put vertex here**

6=a(2+3)²-4------------- **I put x and y intercept here**

6=a(25)-4

6=25a-4

6+4=25a

10/25=25a/25

2/5=a

∴y=2/5(x+3)²-4

## The following Videos shows you how to graph Quadratic function in vertex form

## Video discription

**a**value.

## Video Discription

## This video you see graphing using transformations and mapping notation

## Video Discription

## Word Problem using vertex form

**A baseball is tossed into air and follows the path h= -2t² + 6t, where t is the time, in seconds, and h is the height of the baseball, in metres.**

**a) Find maximum height of baseball?**

**b)At what time baseball reach its maximum height?**

**B) h=-2t²+6t**

**Let h=0**

**0= -4t+6**

**-6=-4t**

**-6/-4=t**

**1.5=t **

**A) -2(1.5)²+6(1.5)**

**h=-2*2.25+9**

**h=-4.5+9**

**h= 4.5**

## Learning Goals

2.Today I learn today how to find an equation.