The function [tex]u(x)=-x+3x^{2} -8[/tex] is a quadratic function due to the highest exponent being 2.
Given functions are:
[tex]u(x)=-x+3x^{2} -8[/tex]
[tex]v(x)=2x^{2} +8x^3+9x[/tex]
[tex]y(x)=x^{2} +3x^5+4[/tex]
[tex]z(x) =7x^{2} +2x^3-3[/tex]
What is a quadratic function?
A function of the form [tex]f(x)=ax^{2} +bx+c[/tex] with [tex]a\neq 0[/tex] is called a quadratic function means the highest exponent of polynomial should be 2.
Let us check one by one.
[tex]u(x)=-x+3x^{2} -8[/tex]
Highest exponent =2
The function is also of form [tex]f(x)=ax^{2} +bx+c[/tex] so u(x) is a quadratic function.
The functions v(x), y(x), and z(x) are having highest exponents as 3,5, and 3 respectively so they are not quadratic functions.
Hence, the function [tex]u(x)=-x+3x^{2} -8[/tex] is a quadratic function due to the highest exponent being 2.
To get more about quadratic functions visit:
https://brainly.com/question/1214333
