How do you find the domain and range of $f(x)=7x^2-11x+9$ ?

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Answer 1 · 2017-10-06T07:26:57

See explanation.

The function is a polynomial, so its domain is $RR$ .

To find the range we have to find the coordinates of the vertex of parabola.

$p=(-b)/(2a)$

$p=11/(2*7)=11/14$

To calculate $q$ we can either use the formula:

Or calculate the value of $f(p)$ by substituting $p$ for $x$ :

$q=f(p)=7*(11/14)^2-11*(11/14)+9$

$q=847/196-121/14+9$

$q=(847-1694+1764)/196$

$q=917/196$

$q=4 133/196$

The coefficient of $x^2$ is positive, so the range is: