Vertex Formula

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A parabola depending upon the given equation opens either upward or downward. The vertex of a parabola is the point where the graph takes a turn and changes its direction. If a parabola opens upward, then the vertex of the parabola is the lowest point or the minimum point on the graph. If the parabola opens downward, then the vertex is the highest point or the maximum point on the graph. We can use the vertex formula in order to find the coordinates of the vertex of the parabola.

Example 1: What is the vertex of the parabola of the equation y= 2x2– 4x+ 5?

The ‘x’ coordinate of the vertex of a parabola is x = -b/2a for an equation of the form    y= ax2+ bx+ c

In the given question, a= 2, b= -4 and c= 5.

Hence the vertex, x= - (-4)/ (2* 2) = 4/4= 1

Now substitute x= 1 in the given equation to get ‘y’.

This gives: y= (2* 12) – (4* 1) + 5= 2- 4+ 5= 3.

Therefore the vertex of the parabola is= (1, 3).

Example 2: What is the vertex of the parabola of the equation y= x2 + 6x + 8?

The ‘x’ coordinate of the vertex of a parabola is x = -b/2a for an equation of the form    y= ax2+ bx+ c

In the given question, a= 1, b= 6 and c= 8.

Hence the vertex, x= - (6)/ (2* 1) = -6/2= -3.

Now substitute x= -3 in the given equation to get ‘y’.

This gives: y= (-32) + (6* -3) + 8= 9- 18 + 8= -1.

Therefore the vertex of the parabola is= (-3, -1).


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