Answer

Verified

407.4k+ views

**Hint:**In this question we need to find the graph of \[y = {\left( {x + 2} \right)^2}\] and determine the transformation for it. To obtain the graph find the value of y for the different value of x and then mark the points on the graph to make the graph. Also to determine the transformation, determine the change in the transformation from parent function to given function.

**Complete Step By Step solution:**

In this question we have given a function that is \[y = {\left( {x + 2} \right)^2}\] and we need to sketch the graph and need to describe the transformation.

The above function is the quadratic function. The parent function for the quadratic function is \[y = {x^2}\].

Consider the table of values for this parent function is,

\[y\] | \[x\] |

\[4\] | \[ - 2\] |

\[9\] | \[ - 3\] |

\[25\] | \[ - 5\] |

\[49\] | \[ - 7\] |

\[64\] | \[ - 8\] |

\[4\] | \[2\] |

\[9\] | \[3\] |

\[25\] | \[5\] |

\[49\] | \[7\] |

\[64\] | \[8\] |

From the above table the graph for the parent function is shown below.

Now we will consider the table of values for this given function is,

\[y = {\left( {x + 2} \right)^2}\] | \[x\] |

\[0\] | \[ - 2\] |

\[1\] | \[ - 3\] |

\[9\] | \[ - 5\] |

\[25\] | \[ - 7\] |

\[36\] | \[ - 8\] |

\[16\] | \[2\] |

\[25\] | \[3\] |

\[49\] | \[5\] |

\[81\] | \[7\] |

\[100\] | \[8\] |

From the above table the graph for the given function is shown in figure below.

From the graph for the parent function and the graph for the given equation. It is concluded that the graph of \[{\left( {x + 2} \right)^2}\] is shifted \[2\] unit to the left from the parent function \[{x^2}\].

**Note:**

As we know that the quadratic equation is the equation that is of the standard from \[a{x^2} + bx + c\]. Here, a and b are the coefficients and c is the constant. In the general equation the highest power of the x is \[2\] so the equation is called quadratic. The range of all the quadratic functions lies from \[ - \infty \] to \[\infty \].

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How do you graph the function fx 4x class 9 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Change the following sentences into negative and interrogative class 10 english CBSE