# How do you find the domain and range of y = 2x^2 - 5x?

Aug 29, 2017

Domain: $x \in \mathbb{R} \mathmr{and} \left(- \infty , \infty\right)$ .
Range: $y \ge - 3.125 \mathmr{and} \left[- 3.125 , \infty\right)$

#### Explanation:

$y = 2 {x}^{2} - 5 x$ . Domain : Any real value of x i.e $x \in \mathbb{R}$

Range: $y = 2 \left({x}^{2} - \frac{5}{2} x\right) = 2 \left({x}^{2} - \frac{5}{2} x + {\left(\frac{5}{4}\right)}^{2}\right) - 2 \cdot \frac{25}{16}$

$y = 2 {\left(x - \frac{5}{4}\right)}^{2} - \frac{25}{8} = 2 {\left(x - 1.25\right)}^{2} - 3.125$

Vertex is at $\left(1.25 , - 3.125\right)$ , Range : $y \ge - 3.125$

Domain: $x \in \mathbb{R} \mathmr{and} \left(- \infty , \infty\right)$

Range: $y \ge - 3.125 \mathmr{and} \left[- 3.125 , \infty\right)$

graph{2x^2-5x [-10, 10, -5, 5]}