Quadratics

Graphing Vertex Form

Index

Summary of vertex form

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

Axis of Symmetry

The axis of symmetry is the vertical line that goes through the vertex of a quadratic equation. .

Optimal value

The minimum (or maximum) value. If the parabola opens upward it is min and if parabola comes down it is max. Value of y in the vertex is optimal value.

What does a tells you about?

If 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?

y = 3(x + 4)² - 6

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.

Big image

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

y = a(x − h)² + k

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?

Find an equation when vertex is (-3,4) and points are (2,6)?

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

Quick Way of Graphing a Quadratic Function in Vertex Form

Video discription

In this video you see how to find vertex in an equation. In this video you also see how to graph parabola with vertex and step pattern. That video tells you about how to find other points using a value.
4.4 Day 1 - Graphing Parabolas in Vertex Form (Part 1)

Video Discription

In the upper video you learn what is vertex , how to find axis of symmetry. This video tells you about how to write tranformations and how to graph vertex equation with given x.

This video you see graphing using transformations and mapping notation

Graphing Quadratic Functions Using Transformations

Video Discription

This video tells you about y=x². How to grph by using transformations. What is mapping notation formula and how it works. How to Graph parabola by using mapping notation.

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

1.Today I learn how to graph using transformations and mapping notation.

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