

Equation of a ParabolaStandard Form and Vertex Form EquationsThis page: Vertex Form Equation  Graph parabola from Vertex Form  Identify Vertex from Equation Standard Form Equation Related Pages: How to convert equations from standard to vertex form and back
The equation of a parabola can be expressed in either standard or vertex form as shown in the picture below.
Standard Form Equation
The standard form of a parabola's equation is generally expressed:
Vertex Form of Equation
The vertex form of a parabola's equation is generally expressed as : y= a(xh)^{2}+k
Practice Problems Vertex and DirectionVertex Form Equation
Part I
1) What is the graph of the following parabola y = (x–1)² + 1?
2) What is the graph of the following parabola y = –(x–1)² + 1?
3) What is the graph of the following parabola y = (x+2)² –3?
Identifying the vertex in vertex form1) What is the vertex of the following parabola: y = (x + 3)² + 4
2) Find the vertex of the following parabola: y = (x  3)² + 4
3) What is the vertex of the parabola whose vertex form equation is y = (x  2)²  3
Part II
1) What is the vertex of a parabola with the following equation: y= 2(x3)^{2}+4 ? Does the parabola open upwards or downwards?
The vertex is (3,4) and it opens upwards since a is positive( it is 2), it opens upwards . 2) If a parabola's equation is y = 3(x+3)^{2} +4, what is its vertex? Which way does it open?
3) A parabola has the equation y = 22(x  9)^{2} + 5. What is its vertex? Which way does the parabola open?
