Question

If $p\left(x\right)=4x^2-5x+6$ find range between $-1$ and $2$

Answer 1

range of $4x^2-5x+6$ in $(-1,2)$

$p\left(x\right)=4x^2-5x+5$

$p\left(x\right)=8x-5=0$

$x=\frac{5}{8}$

$p\left(x\right)=8=positive$

Min $p\left(x\right)=4\times {\left(\frac{5}{8}\right)}^2-5\times \frac{5}{8}+6=\frac{71}{16}$

$p(-1)=4+5+6=15$

$p\left(2\right)=16-10+6=12$

$p\left(x\right)$ Range if from $(\frac{71}{16},15)$