New In our Forum
isosceles trapezoid by 9fires
Re: average pie method by smoke60
Math Video Game! Play Fraction Balls!

A+    A−    B  
Home Page
Algebra
Games
Geometry
Interactive
Trigonometry
Forum
Math Jobs




AddThis Social Bookmark Button

Converting the Equation of Parabola: Vertex and Standard Forms

From Vertex To Standard Form

This page: Vertex Form Equation | Graph parabola from Vertex Form | Identify Vertex from Equation
Standard Form Equation
Related Pages: Parabola--graph, equation and formula |Axis of Symmetry |Standard and Vertex Forms of Equation| real world applications | Converting between Standard and Vertex Forms | Interactive Parabola(click and drag) | area of parabola
 Standard Form Equation 
The standard form of a parabola's equation is generally expressed:
  • y = ax 2 + bx + c
    • The role of 'a'
      • If a> 0, the parabola opens upwards
      • if a< 0, it opens downwards.
    • The axis of symmetry
Standard Form Equation Role
 Vertex Form of Equation  
The vertex form of a parabola's equation is generally expressed as :
y= a(x-h)2+k
  • (h,k) is the vertex
  • If a is positive then the parabola opens upwards like a regular "U".
  • If a is negative, then the graph opens downwards like an upside down "U".
  • If |a| > 1, the graph of the parabola widens. This just means that the "U" shape of parabola stretches out sideways .
  • If |a| < 1, the graph of the graph becomes narrower(The effect is the opposite of |a| > 1).
This page: Vertex Form Equation | Graph parabola from Vertex Form | Identify Vertex from Equation
Standard Form Equation
Related Pages: Parabola--graph, equation and formula |Axis of Symmetry |Standard and Vertex Forms of Equation| real world applications | Converting between Standard and Vertex Forms | Interactive Parabola(click and drag) | area of parabola

 From Vertex To Standard Form  



Example of how to convert the equation of a parabola from vertex to standard form.
Equation in vertex form : y = (x – 1)²
To convert equation to standard form simply expand and simplify the binomial square (Refresher on FOIL to multiply binomials)

picture from vertex to standard form equation parabola
Parabola 1 has the vertex form equation :
    y = (x + 3)²
  • To rewrite this equation in standard form
    • Expand (x+3)(x+3)
      Answer

2. Change the parabola's equation from vertex form to standard form.
    y = (x + 3)² + 4
    Answer

3. Change the parabola's equation from vertex form to standard form.
    y = (x - 3 )² + 2
    Answer

4. Convert the equation below from vertex form to standard form.
y - 4 = (x - 3 )²
    Answer



5. Change the equation of the parabola below into standard form
y - 3 = (x - 5 )²
    Answer

Standard Form to Vertex Form

To convert an equation from standard form to vertex form it is sometimes necessary to be comfortable completing the square.
Convert the equation below from standard to vertex form.
1. y = x² + 2x + 1
    Answer
What is the vertex form of the parabola whose standard form equation is
2. y = x² + 6x +9
    Answer
What is the vertex form of the parabola whose standard form equation is
3. y = x² + 6x + 10
    Answer
Convert the equation below from standard to vertex form.
4. y = x² + 6x + 8
    Answer
What is the vertex form of the parabola whose standard form equation is
5. y = x² + 10x + 25
    Answer
What is the vertex form of the parabola whose standard form equation is
6. y = x² + 10x + 27
    Answer
What is the vertex form of the parabola whose standard form equation is
7. y = x² + 10x + 21
    Answer
Convert the equation below from standard to vertex form.
8. y = x² + 12x + 34
    Answer
What is the vertex form of the parabola whose standard form equation is
9. y = x² + 14x + 40
    Answer
Convert the equation below from standard to vertex form.
10. y = x² + 18x + 71
    Answer
What is the vertex form of the parabola whose standard form equation is
11. y = x² – 16x + 71
    Answer
What is the vertex form of the parabola whose standard form equation is
12. y = x² + 18x + 95
    Answer
Convert the equation below from standard to vertex form.
13. y = x² – 20x + 95
    Answer


When "a" is not zero!



Convert the parabola's equation below to vertex form.
14. y = 2x² + 4x + 5
    Answer
Complete the square to convert the equation into vertex form.
15. y =2x² + 4x + 6
    Answer
Convert the parabola's equation below to vertex form.
16. y = 3x² + 6x + 8
    Answer
Top
Welcome Guest
Please Log in or register
Who's online: 11 Guests, 0 Users :        Please welcome 9fires, our newest member.
AddThis Social Bookmark Button Page copy protected against web site content infringement by Copyscape
copyright & terms of use | site map | about