
The vertex form of a quadratic equation is f(x) = a(x  h)^{2} + k. This form is called the vertex form because the point (h, k) is the vertex of the parabola described by the equation. 
An advantage of transforming a quadratic equation into vertex form is that it is easier to graph. Since the vertex can be read from the equation, it can quickly be identified and plotted.
General Case  Example  Description 

y = a((h + 1)  h)^{2} + k  y = 1((2 + 1)  2)^{2} + 1  Substitute h + 1 in for x. 
y = a(h  h + 1)^{2} + k  y = 1(3  2)^{2} + 1  Simplify the innermost parenthesis. 
y = a · 1^{2} + k  y = 1 · 1^{2} + 1  Simplify the remaining parenthesis. 
y = a · 1 + k  y = 1 · 1 + 1  Simplify the exponent. 
y = a + k  y = 1 + 1  Simplify the multiplication. 
y = k + a  y = 0  Simplify the addition and subtraction. 
So, (h + 1, k + a) is a point on the graph.  So, (3, 0) is a point on the graph.  Plot the point. 
Table 1: Plot (h + 1, k + a). 
General Case  Example  Description 

y = a((h  1)  h)^{2} + k  y = 1((2  1)  2)^{2} + 1  Substitute h + 1 in for x. 
y = a(h  h  1)^{2} + k  y = 1(1  2)^{2} + 1  Simplify the innermost parenthesis. 
y = a(1)^{2} + k  y = 1(1)^{2} + 1  Simplify the remaining parenthesis. 
y = a · 1 + k  y = 1 · 1 + 1  Simplify the exponent. 
y = a + k  y = 1 + 1  Simplify the multiplication. 
y = k + a  y = 0  Simplify the addition and subtraction. 
So, (h  1, k + a) is a point on the graph.  So, (1, 0) is a point on the graph.  Plot the point. 
Table 1: Plot (h  1, k + a). 
Click on the points on the sliders and drag them to change the figure. Click on the check boxes to see each step. 
Manipulative 2  How to Graph a Quadratic Equation in Vertex Form Created with GeoGebra. 
Often it is easier to sketch a quadratic equation by converting it to vertex form. This can be done using complete the square.
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