Vertex form of the quadratic equation

🏆Practice vertex representation

Vertex form of the quadratic equation

The vertex form allows us to identify, very easily, the vertex of the parabola and hence its name.

The vertex form of the quadratic function is:
Y=a(X−p)2+cY=a(X-p)^2+c

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\( f(x)=(x-3)^2+x \)

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Where the values of the vertex of the parabola are (p,c)( p,c)
PP - represents the value of the XX of the vertex.
CC - represents the value of the YY of the vertex.
For example in the function:
Y=2(X−3)2+5Y=2(X-3)^2+5

The vertex of the parabola is:
(3,5)(3,5)

Observe
In the formula for the vertex form there is a minus sign before PP. This is how the template is constructed, it does not mean that PP is negative.
If we obtain a negative XX vertex we will place it with a minus sign in the vertex form template and the minus will turn into plus.


Examples and exercises with solutions of the vertex form of the quadratic function

Exercise #1

f(x)=(x−3)2+x f(x)=(x-3)^2+x

Video Solution

Answer

f(x)=x2−5x+9 f(x)=x^2-5x+9

Exercise #2

Find the vertex of the parabola

y=x2−6 y=x^2-6

Video Solution

Answer

(0,−6) (0,-6)

Exercise #3

Find the vertex of the parabola

y=(x−3)2 y=(x-3)^2

Video Solution

Answer

(3,0) (3,0)

Exercise #4

Find the vertex of the parabola

y=(x+1)2 y=(x+1)^2

Video Solution

Answer

(−1,0) (-1,0)

Exercise #5

Find the vertex of the parabola

y=(x−1)2−1 y=(x-1)^2-1

Video Solution

Answer

(1,−1) (1,-1)

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