

Converting the Equation of Parabola: Vertex and Standard FormsFrom Vertex To Standard Form
The standard form of a parabola's equation is generally expressed:
$
y = ax^2 + bx + c
$
The role of a in $$ \color{Red}{a}x^2 + bx + c $$
Axis of Symmetry in Standard FormThe axis of symmetry is the line x = b/2a Vertex Form
The vertex form of a parabola's equation is generally expressed as : $ y= a(xh)^ 2 + k $
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)²To convert equation to standard form simply expand and simplify the binomial square (Refresher on FOIL to multiply binomials)
Parabola 1 has the vertex form equation :
2. Change the parabola's equation from vertex form to standard form.
3. Change the parabola's equation from vertex form to standard form.
4. Convert the equation below from vertex form to standard form. y  4 = (x  3 )²
5. Change the equation of the parabola below into standard form y  3 = (x  5 )²
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 What is the vertex form of the parabola whose standard form equation is 2. y = x² + 6x +9 What is the vertex form of the parabola whose standard form equation is 3. y = x² + 6x + 10 Convert the equation below from standard to vertex form. 4. y = x² + 6x + 8 What is the vertex form of the parabola whose standard form equation is 5. y = x² + 10x + 25 What is the vertex form of the parabola whose standard form equation is 6. y = x² + 10x + 27 What is the vertex form of the parabola whose standard form equation is 7. y = x² + 10x + 21 Convert the equation below from standard to vertex form. 8. y = x² + 12x + 34 What is the vertex form of the parabola whose standard form equation is 9. y = x² + 14x + 40 Convert the equation below from standard to vertex form. 10. y = x² + 18x + 71 What is the vertex form of the parabola whose standard form equation is 11. y = x² – 16x + 71 What is the vertex form of the parabola whose standard form equation is 12. y = x² + 18x + 95 Convert the equation below from standard to vertex form. 13. y = x² – 20x + 95 When "a" > 1
Convert the parabola's equation below to vertex form.
Practice Problems 14. y = 2x² + 4x + 5 Complete the square to convert the equation into vertex form. 15. y =2x² + 4x + 6 Convert the parabola's equation below to vertex form. 16. y = 3x² + 6x + 8 