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How do you graph \[y=-{{x}^{2}}+5\]?

seo-qna
Last updated date: 21st Jun 2024
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Answer
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Hint: To solve this question of finding the graph of a function \[y=-{{x}^{2}}+5\], we will be using the basic concept, that is we will find few points on the graph which would satisfy the given equation. We must be having knowledge of the concept of parabola and its applications and properties. By using the general solution technique of assigning different values to the parameters of the given question that is the x and y in the equation we can get the graph.

Complete step-by-step answer:
We will start by finding some points that would lie on the graph of the function. It will help us plot the graph which is asked in the question.
Let us take the value of \[x=0\]. By substituting in given function, we get the value of the y as
\[\Rightarrow y=5\]
In the same way we must also find another reading to get the entire idea of how the graph is going to be, so that we can plot it in a graph.
Let us take the value of \[x=1\] . By substitution, we are able to get the value of y as
\[\Rightarrow y=4\]
So by the basic technique of assigning the different values to x we have found some values of y. Now, with the help of the points we determine the graph as follows,
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Note: The problems of this sort can be done by having the basic knowledge in plotting of a graph by finding the different points on graph using assigning different values and also it can be done by another means of way by having the concept of parabola .from comparing the given equation \[y=-{{x}^{2}}+5\]to the standard form of the parabola that is \[y=a{{\left( x-h \right)}^{2}}+k\]where h,k are vertices .By comparing we get\[\Rightarrow a=-1,h=0,k=5\] and a is negative so parabola will be inverted.