HOW TO FIND VERTEX OF QUADRATIC FUNCTION

How to Find Vertex of Quadratic Function :

Here we are going to see some example problems to understand finding vertex of a quadratic function.

How to Find Vertex of Quadratic Function ?

To find the vertex form of the parabola, we use the concept completing the square method.

Vertex form of a quadratic function :

y = a(x - h)2 + k

In order to find the maximum or minimum value of quadratic function, we have to convert the given quadratic equation in the above form.

To find vertex using completing the square method, please visit the page "How to Find the Minimum or Maximum Value of a Function in Vertex Form"

Finding Vertex of a Quadratic Function - Examples

Question 1 :

Find the vertex of the graph of the given function f.

f(x) = 7x2 − 12

Solution :

We may write the given equation as,

f(x) = 7(x - 0)2 − 12

y = a(x - h)2 + k

By comparing the above equation with vertex form, we get

Vertex (h, k)  ==>  (0, -12)

(ii)  f(x) = −9x2 − 5

Solution :

We may write the given equation as,

f(x) = −9(x - 0)2 − 5

y = a(x - h)2 + k

By comparing the above equation with vertex form, we get

Vertex (h, k)  ==>  (0, -5)

(iii)  f(x) = (x − 2)2 − 3

Solution :

We may write the given equation as,

f(x) = (x − 2)2 − 3

y = a(x - h)2 + k

By comparing the above equation with vertex form, we get

Vertex (h, k)  ==>  (2, -3)

(iv)  f(x) = (x + 3)2 + 4

Solution :

We may write the given equation as,

f(x) = (x + 3)2 + 4

y = a(x - h)2 + k

By comparing the above equation with vertex form, we get

Vertex (h, k)  ==>  (-3, 4)

(v)  f(x) = (2x − 5)2 + 6

Solution :

We may write the given equation as,

f(x) = (2x − 5)2 + 6

f(x)  =  4x2 - 2(2x) (5) + 52 + 6

f(x)  =  4x2 - 20x + 25 + 6

f(x)  =  4x2 - 20x + 31

f(x)  =  4[x2 - 5x] + 31

f(x)  =  4[x2 - 2⋅x⋅(5/2) + (5/2)2 - (5/2)2] + 31

f(x)  =  4[x + (5/2)]2 - 4(25/4) + 31

f(x)  =  4[x + (5/2)]2 + 6

y = a(x - h)2 + k

By comparing the above equation with vertex form, we get

Vertex (h, k)  ==>  (-5/2, 6)

(vi)  f(x) = (7x + 3)2 + 5

Solution :

We may write the given equation as,

f(x) = (7x + 3)2 + 5

=  72 (x + (3/7))2 + 5

=  49 (x + (3/7))2 + 5

y = a(x - h)2 + k

By comparing the above equation with vertex form, we get

Vertex (h, k)  ==>  (-3/7, 5)

After having gone through the stuff given above, we hope that the students would have understood "How to Find Vertex of Quadratic Function".

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