**Domain and range of quadratic function worksheet : **

Worksheet on domain and range of quadratic function is much useful to the students who would like to practice problems on quadratic functions.

1. Find the domain and range of the quadratic function given below.

y = x² + 5x + 6

2. Find the domain and range of the quadratic function given below.

y = -2x² + 5x - 7

**Problem 1 : **

Find the domain and range of the quadratic function given below.

y = x² + 5x + 6

**Solution : **

**Domain : **

In the quadratic function, y = x² + 5x + 6, we can plug any real value for "x".

Because, "y" is defined for all real values of "x"

Therefore, the domain of the given quadratic function is all real values.

That is,

**Domain = { x | x ∈ R }**

**Range : **

When we compare the given quadratic function with y = x² + 5x + 6, we get

a = 1

b = 5

c = 6

Since the leading coefficient "a" is positive, the parabola is open upward.

"x" coordinate of the vertex = -b / 2a

"x" coordinate of the vertex = -5 / 2(1)

"x" coordinate of the vertex = -5 / 2

"x" coordinate of the vertex = -2.5

"y" coordinate of the vertex = y(-2.5)

"y" coordinate of the vertex = (-2.5)² + 5(-2.5) + 6

"y" coordinate of the vertex = 6.25 - 12.5 + 6

"y" coordinate of the vertex = -0.25 or -1/4

**Vertex ( -2.5, -0.25 )**

Since the parabola is open upward, range is all the real values greater than or equal to -1/4

**Range = { y | y ≥ -0.25 }**

To have better understanding on domain and range of a quadratic function, let us look at the graph of the quadratic function y = x² + 5x + 6.

When we look at the graph, it is clear that "x" (Domain) can take any real value and "y" (Range) can take all real values greater than or equal to -0.25

**Problem 2 : **

Find the domain and range of the quadratic function given below.

y = -2x² + 5x - 7

**Solution : **

**Domain :**

In the quadratic function, y = -2x² + 5x - 7, we can plug any real value for "x".

Because, "y" is defined for all real values of "x"

Therefore, the domain of the given quadratic function is all real values.

That is,

**Domain = { x | x ∈ R }**

**Range : **

When we compare the given quadratic function with y = -2x² + 5x - 7, we get

a = -2

b = 5

c = -7

Since the leading coefficient "a" is negative, the parabola is open downward.

"x" coordinate of the vertex = -b / 2a

"x" coordinate of the vertex = -5 / 2(-2)

"x" coordinate of the vertex = -5 / (-4)

"x" coordinate of the vertex = 1.25

"y" coordinate of the vertex = y(1.25)

"y" coordinate of the vertex = -2(1.25)² + 5(1.25) - 7

"y" coordinate of the vertex = -3.125 + 6.25 - 7

"y" coordinate of the vertex = -3.875

**Vertex ( 1.25, -3.875 )**

Since the parabola is open downward, range is all the real values less than or equal to -3.875

**Range = { y | y ****≤**** -3.875 }**

To have better understanding on domain and range of a quadratic function, let us look at the graph of the quadratic function y = -2x² + 5x - 7.

When we look at the graph, it is clear that "x" (Domain) can take any real value and "y" (Range) can take all real values less than or equal to -3.875

After having gone through the stuff given above, we hope that the students would have understood "Domain and range of quadratic function worksheet".

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