The equation y = [tex]6x -3\sqrt{x}[/tex] is not a quadratic function .
What is quadratic function?
A quadratic function is a polynomial of degree 2 and so the equation of quadratic function is of the form f(x) = ax² + bx + c, where 'a' is a non-zero number; and a, b, and c are real numbers. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape
According to the question
To check equation is quadratic function or not.
For that we will draw the graph of all the equation
As we know The graph of a quadratic function is a curve called a parabola and it will always a parabola .
a> [tex]y = \frac{1}{x^{2} +5} - 3[/tex]
x y
0 -2.8
1 -2.83
-1 -2.83
The graph of this equation is a parabola .
Therefore,
It is a quadratic function .
b> [tex]x^{2} = y -1[/tex]
or
[tex]x^{2} + 1 = y[/tex]
x y
0 1
1 2
-1 2
The graph of this equation is a parabola .
Therefore,
It is a quadratic function .
c> [tex]y = 3x - 7 + 4x^{2}[/tex]
x y
0 -7
1 0
-1 -6
The graph of this equation is a parabola .
Therefore,
It is a quadratic function .
d> y = [tex]6x -3\sqrt{x}[/tex]
x y
0 0
1 3
4 18
In this we cannot take negative values as square root makes -ve into imaginary number .
The graph of this equation is not a parabola .
Therefore,
It is not a quadratic function .
Hence, The equation y = [tex]6x -3\sqrt{x}[/tex] is not a quadratic function .
To know more about quadratic function here:
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