How do you find the range of $f(x)=5x^2+2x-1$ ?

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Answer 1 · 2015-08-14T15:25:23

Range: ${f(x) in RR: f(x) >= -6/5}$

$f(x) = 5x^2 + 2x - 1$

Method 1: Completing the squares
$f(x)= 5(x^2 + 2/5x + 1/25 - 1/25) - 1$
$= 5(x + 1/5)^2 - 6/5$

Method 2: Stationary points
$f'(x)= 0$
$10x = -2$
$x = -1/5, f(-1/5) = -6/5$

Minimum point $(-1/5,-6/5)$

Hence range: ${f(x) in RR: f(x) >= -6/5}$

graph{5x^2+2x-1 [-2, 2, -5, 5]}

How do you find the range of f(x)=5x^2+2x-1f(x)=5x^2+2x-1?