# What is the range of the function y=4x^2+2?

May 8, 2018

See explanation.

#### Explanation:

Graph of this function is a parabola with vertex at $\left(0 , 2\right)$. The function's values go to $+ \infty$ if $x$ goes to either $- \infty$ or $+ \infty$, so the range is:

## $r = \left(2 , + \infty\right)$

The graph is:

graph{4x^2+2 [-10, 10, -5, 5]}

May 8, 2018

Range: $\left[+ 2 , + \infty\right)$

#### Explanation:

$y = 4 {x}^{2} + 2$

$y$ is a quadratic function of the form $a {x}^{2} + b x + c$
Where: $a = + 4 , b = 0 \mathmr{and} c = + 2$

$y$ will have a parabolic graph with axis of symmetry where $x = - \frac{b}{2 a}$

$\therefore x = 0$

Since $a > 0$ $y$ will have a minimum value at $x = 0$

$\therefore {y}_{\min} = + 2$

Since, $y$ has no finite upper bound the range of $y$ is $\left[+ 2 , + \infty\right)$