1. ## Maximum/Minimum value of a quadratic expression

State the minimum or maximum value of y and the corresponding value of x for
y=4(x^2) + 2 .

2. $4> 0\Rightarrow \displaystyle f:\mathbb{R} \mapsto \mathbb{R}, f(x)=4x^{2}+2$ has a minimum, it is obtained for $x=-\frac{0}{2\cdot4 }=0$, $y=\frac{-\Delta }{4\cdot4}=2$

3. Originally Posted by Ilsa
State the minimum or maximum value of y and the corresponding value of x for
y=4(x^2) + 2 .
$y = 4(x - 0)^2 + 2$

compare your equation to the vertex form of a quadratic equation ...

$y = a(x - h)^2 + k$

where the vertex is the point $(h,k)$

since $a > 0$ , $x = h$ is the vertex location and $y = k$ is the corresponding minimum value