the range of this quadratic function y=-x^2+6x-2

fumefluosault7pa

fumefluosault7pa

Answered question

2022-02-01

the range of this quadratic function
y=x2+6x2

Answer & Explanation

budniji8d1

budniji8d1

Beginner2022-02-02Added 15 answers

Given function is:
f(x)=x2+6x2
which is a quadratic function, whose graph is a parabola.
To find the critical points of f(x).
Let
acute{f}(x)=0
2x+6=0
2x=6
x=3
is the only critical value.
We can either use the knowledge of quadratics or take the second derivatives f(x)=2
f(3)=2<0
So, at x=3, the function has maximum.
And the maximum value is
f(3)=32+6(3)2
=9+182
=7
So, the range of the given quadratic function is[,7]

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