# What is the domain and range of g(x) = x^2 + 7x -18 ?

Sep 20, 2015

Domain is all $x \in \mathbb{R}$
Range is {yinRR|y>=-121/4}=[-121/4;oo)

#### Explanation:

This is a 2nd degree quadratic polynomial so its graph is a parabola.

Its general form is $y = a {x}^{2} + b x + c$ where in this case a = 1 indicating that the arms go up, b = 7, c = - 18 indicating the graph has y-intercept at - 18.

The domain is all possible x values that are allowed as inputs and so in this case is all real numbers $\mathbb{R}$ .

The range is all possible output y values that are allowed and so since the turning point occurs when the derivative equals zero,
$\implies 2 x + 7 = 0 \implies x = - \frac{7}{2}$
The corresponding y value is then $g \left(- \frac{7}{2}\right) = - \frac{121}{4}$

Hence the range {yinRR|y>=-121/4}=[-121/4;oo)

I have included the graph underneath for extra clarity.

graph{x^2+7x-18 [-65.77, 65.9, -32.85, 32.9]}