Lessons On Parabolas And Quadratics

Everything on vertex, factored, and standard form

About The Site

In this website, I will be showing all the lessons you need to know to learn all types of parabolas. This site will include all the formulas, examples, charts and graphs. After studying this website you will have the knowledge to pass grade 10 academic math.

Table Of Contents

  • UNIT #1: Vertex Form
  • UNIT #2: Factored Form
  • UNIT #3: Standard Form
  • MY REFLECTION

1. Graphing Vertex Form

Summary Of Unit

Vertex Form: y =a (x - h)² + k

Vertex form is a formula which is used to determine what the vertex is and where the vertex is located, and it also determines the a value which helps you find the width of the graph. In this unit who will find that the h variable represents the x-intercept, the K variable represents the y-intercept and the a variable represents the width of the parabola.

Learning Goals

My learning goals are


  • to be able to identify any vertex forms and all the points and intersects, i should be able to determine and K,H, and A points\
  • to be able to make a graph plotting all the variables with vertex form
  • to determine the equation from a word problem

Graph For Vertex Form

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Word Problem For Vertex Form

Jack draws a rainbow which is a parabola that has the equation y =-0.1(x-1)2+6, where x and y are measured in centimeters. If the height of the rainbow is 6 cm, how far away are the end points of the rainbow from one another?
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A:The vertex of the rainbow is (1,6), which is A. The distance from the left end point of the rainbow to the right end point is the distance from B to C.

0 =-0.1(x-1)2+6

x = 8.75 or -6.75

Therefore, the total distance between the two end points is 8.75 + 6.75 = 15.5 cm.

Video For Graphing Transformations

Transformations - Graphing from Vertex Form

Factored Form

Learning Goals

  • I want to be able to expand and simply factored equations
  • I want to be able to graph factored form equations and find the zeroes
  • I want to be able to solve perfect squares

Summary of unit

y=a(x-r)(x-s)

Factoring is a form which can be done in a number of ways such as factoring by grouping, expanding and simplifying, using trinomials and solving perfect squares, there are lots of other ways to. The purpose for using factoring form can be to break down trinomials and find the x-intercepts so it will be possible to graph parabolas. To find the zeroes you have to solve for the x intercepts.

Various Factoring examples

SIMPLE FACTORING

x2 + 5x + 6 = x2 + 3x + 2x + 6
= (x2 + 3x) + (2x + 6)
= x(x + 3) + 2(x + 3)
= (x + 3)(x + 2)


FACTORING BY GROUPING

y2 + 35x + 7y + 5xy

=y2 + 7y + 35x + 5xy

=y(y + 7) + 5x(7 + y)

=y(y + 7) + 5x(y + 7)

=(y + 5x)(y + 7)

Word Problem


Jennifer hit a golf ball from the ground and it followed the projectile , where t is the time in seconds, and h is the height of the ball. Find the highest point that her golf ball reached and also when it hits the ground again. Find a reasonable domain and range for this situation.

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Video

Factoring Complex Trinomials

Standard Form

Learning Goals

  • I need to be able to determine the a variable which gives me the shape and direction of the opening
  • I need to be able to find the value of c which is the y-intercept
  • I need to be able to solve using the quadratic formula, to get the x-intercepts.
  • I need to be able to find the max or min, and complete the square to determine vertex form

Summary Of The Unit

ax2 + bx + c = 0

Standard form is mostly used as a method to determine the x intercepts,a standard from equation can be subbed into a quadratic formula to find the x intercepts which can be used when graphing a parabola. Standard form also helps us determine the max and min.

Quadratic formula

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Perfect Square

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Word Problem

A garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters. What will be the width of the pathway?

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4x2 + 56x - 93 = 0

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Video

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Final Submission

Quadratics Reflection

All three units, vertex form, standard form, and factored form, are all connected to parabolas. For example Standard form has the y intercept in it, and to graph a parabolas you need to go to vertex form to get the additional information like the vertex, so that you can graph it. Another connection is between Vertex and Factored form, for example you can get the x intercepts in factored form and use them with the help of vertex form to plot the graph. the quadratic connections come into play when we are subbing the standard form equation into the quadratic formula to determine the x intercepts which help us graph the parabola.Also, by expanding and simplifying vertex from using factoring, you can go to standard form, which is another connection between the three units. In my opinion the easiest unit for me was factored form and the hardest was vertex form.

FACTORED FORM TEST

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