Answer
Verified
426.6k+ views
Hint:In the given question, we have to find the x intercepts of the quadratic function in coordinate form. The x intercept of a quadratic equation is the point where the curve meets the x axis. We know that the y coordinate of any point on the x axis is zero. So, we have to find the value of x coordinate when the value of y is zero. So, we substitute y as zero in the given function and find the corresponding values of x. The value of x can be found by using the method of transposition.
Complete step by step answer:
So, the given function is: ${\left( {x + 4.5} \right)^2} - 6.25 = y$
We substitute the value of y as zero to find the x intercept.
So, ${\left( {x + 4.5} \right)^2} - 6.25 = 0$
Shifting $6.25$ to right side of the equation,
$ \Rightarrow {\left( {x + 4.5} \right)^2} = 6.25$
Now, we take the square root of both sides of the equation.
$\Rightarrow \left( {x + 4.5} \right) = \pm \sqrt {6.25} $
Now, we shift $4.5$ to right side of the equation,
$ \Rightarrow x = \pm \sqrt {6.25} - 4.5$
We know that the value of $\sqrt {6.25} $ is $2.5$.
Hence, $x = \pm 2.5 - 4.5$
$\therefore x = 2$ or $x = - 7$
Hence, the x intercepts of the quadratic function in coordinate form in the function ${\left( {x + 4.5} \right)^2} - 6.25 = y$ is $\left( {2,0} \right)$ and $\left( { - 7,0} \right)$.
Note: Method of transposition involves doing the exact same mathematical thing on both sides of an equation with aim of simplification in mind. This method can be used to solve various algebraic equations like the one given in question with ease.
Complete step by step answer:
So, the given function is: ${\left( {x + 4.5} \right)^2} - 6.25 = y$
We substitute the value of y as zero to find the x intercept.
So, ${\left( {x + 4.5} \right)^2} - 6.25 = 0$
Shifting $6.25$ to right side of the equation,
$ \Rightarrow {\left( {x + 4.5} \right)^2} = 6.25$
Now, we take the square root of both sides of the equation.
$\Rightarrow \left( {x + 4.5} \right) = \pm \sqrt {6.25} $
Now, we shift $4.5$ to right side of the equation,
$ \Rightarrow x = \pm \sqrt {6.25} - 4.5$
We know that the value of $\sqrt {6.25} $ is $2.5$.
Hence, $x = \pm 2.5 - 4.5$
$\therefore x = 2$ or $x = - 7$
Hence, the x intercepts of the quadratic function in coordinate form in the function ${\left( {x + 4.5} \right)^2} - 6.25 = y$ is $\left( {2,0} \right)$ and $\left( { - 7,0} \right)$.
Note: Method of transposition involves doing the exact same mathematical thing on both sides of an equation with aim of simplification in mind. This method can be used to solve various algebraic equations like the one given in question with ease.
Recently Updated Pages
Identify the feminine gender noun from the given sentence class 10 english CBSE
Your club organized a blood donation camp in your city class 10 english CBSE
Choose the correct meaning of the idiomphrase from class 10 english CBSE
Identify the neuter gender noun from the given sentence class 10 english CBSE
Choose the word which best expresses the meaning of class 10 english CBSE
Choose the word which is closest to the opposite in class 10 english CBSE
Trending doubts
A rainbow has circular shape because A The earth is class 11 physics CBSE
Which are the Top 10 Largest Countries of the World?
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Change the following sentences into negative and interrogative class 10 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
What organs are located on the left side of your body class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE