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How do we find the x intercepts of a quadratic function in coordinate form in the function ${\left( {x + 4.5} \right)^2} - 6.25 = y$ ?

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Last updated date: 01st Mar 2024
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IVSAT 2024
Answer
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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.
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