VERTEX FORM OF A QUADRATIC FUNCTION WORKSHEET

1. Write the quadratic function in vertex form whose graph is shown below.

practice worksheet graphing quadratics in vertex form

Questions 2-4 : Write the quadratic function in vertex form and write its vertex.

2. f(x) = x 2  + 6x + 9

3. f(x) = -x 2  - 2x - 2

4. f(x) = 4x 2  + 16x + 5

5.  Write the following quadratic function in vertex form and sketch its graph :

f(x) = -x 2  + 2 x + 3

practice worksheet graphing quadratics in vertex form

1. Answer :

The parabola above opens up with vertex (2, 1).

Vertex form of a quadratic function :

f(x) = a(x - h) 2 + k

Substitute vertex (h, k) = (2, 1).

f(x) = a(x - 2) 2 + 1 ----(1)

The y-intercept of the parabola is (0, 5). That is, the parabola is passing through (0, 5).

Substitute x = 0 and y = 5.

5 = a(0 - 2) 2 + 1

5 = a(- 2) 2  + 1

5 = 4a + 1

Subtract 1 from both sides.

Divide both sides by 4.

Substitute a = 1 in (1).

f(x) = 1(x - 2) 2  + 1

2. Answer :

Vertex form of the quadratic function :

f(x) = x 2  + 6x + 9

f(x) = x 2  + 2(x)(3) + 3 2

f(x) = (x + 3) 2

Comparing  y = a(x - h) 2  + k and  f(x) = (x + 3) 2 ,

h = -3 and k = 0

So, the vertex is (h, k) = (-3, 0).

3. Answer :

f(x) = -x 2  - 2 x - 2

f(x) = -(x 2  + 2x) - 2

f(x) = -[x 2  + 2(x)(1) + 1 2  - 1 2 ] - 2

f(x) = -[(x + 1) 2  - 1 2 ] - 2

f(x) = -[(x + 1) 2  - 1] - 2

f(x) = -(x + 1) 2  + 1 - 2

f(x) = -(x + 1) 2  - 1

Comparing f(x)  = a(x - h) 2  + k and f(x) = -(x + 1) 2  - 1,

h = -1 and k = -1

So, the vertex is (h, k) = (-1, -1).

4. Answer :

f(x) = 4x 2  + 16x + 5

f(x) = 4(x 2  + 4x) + 5

f(x) = 4[x 2  + 2(x)(2) + 2 2  - 2 2 ] + 5

f(x) = 4[(x + 2) 2  - 2 2 ] + 5

f(x) = 4[(x + 2) 2  - 4] + 5

f(x) = 4(x + 2) 2  - 16 + 5 

f(x) = 4(x + 2) 2  - 11

Comparing f(x)  = a(x - h) 2  + k and f(x) = 4(x + 2) 2  - 11,

h = -2 and k = -11

So, the vertex is (h, k) = (-2, -11).

5. Answer :

Vertex form of the quadratic equation :

f(x) = -(x 2  - 2x) + 3

f(x) = -[x 2  - 2(x)(1) + 1 2  - 1 2 ] + 3

f(x) = -[(x - 1) 2  - 1 2 ] + 3

f(x) = -[(x - 1) 2  - 1] + 3

f(x) = -(x - 1) 2  + 1 + 3

f(x) = -(x - 1) 2  + 4

Comparing  f(x)  = a(x - h) 2  + k and  f(x)  = -(x - 1) 2  + 4,

h = 1 and k = 4

So, the vertex is (h, k) = (1, 4).

To graph the above quadratic equation, we need to find x-intercept and y-intercept, if any.

x-intercept :

To find the x-intercept, substitute f(x) = 0.

0 = -(x - 1) 2  + 4

(x - 1) 2  = 4

Take square root on both sides.

x - 1 = ±√4

x - 1 =  ±2

x - 1 = -2  or  x - 1 = 2

x = -1  or  x = 3

So, the x-intercepts are (-1, 0) and (3, 0) .

y-intercept :

To find the y-intercept, substitute x = 0.

f(0) = -(0 - 1) 2  + 4

= -(-1) 2  + 4

= -1 + 4

So, the y-intercept is (0, 3).

Comparing f(x)  = a(x - h) 2  + k and  f(x)  = -(x - 1) 2  + 4,

So, the parabola opens down with vertex (1, 4), x-intercepts (-1, 0) and (3, 0) and y-intercept (0, 3).

practice worksheet graphing quadratics in vertex form

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Practice Worksheet Graphing Quadratics In Vertex Form

Practice Worksheet Graphing Quadratics In Vertex Form – This Quadratic Worksheet will help you with quadratic equations. It will help you learn how to solve quadratic equations by using the quadratic formula. This formula is the most efficient way to solve quadratic equations. There are however other methods to solve quadratic problems, such as graphing, factoring or completing the square. To make solving quadratic equations more efficient, algorithms were developed.

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Graphing Parabolas In Vertex Form Worksheet PICTURETHISEVERYDAYBEAUTY

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