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

Oct 6, 2017

See explanation.

#### Explanation:

The function is a polynomial, so its domain is $\mathbb{R}$.

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

## $p = \frac{- b}{2 a}$

$p = \frac{11}{2 \cdot 7} = \frac{11}{14}$

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

## $q = \frac{- \Delta}{4 a}$

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

$q = f \left(p\right) = 7 \cdot {\left(\frac{11}{14}\right)}^{2} - 11 \cdot \left(\frac{11}{14}\right) + 9$

$q = \frac{847}{196} - \frac{121}{14} + 9$

$q = \frac{847 - 1694 + 1764}{196}$

$q = \frac{917}{196}$

$q = 4 \frac{133}{196}$

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