# 3.6 Quadratic Function, SPM Practice (Short Question)

Question 3:
The straight line y = 5x – 1 does not intersect with the curve y = 2x2 + x + h.
Find the range of values of h.

Solution:

Question 4:
Find the maximum value of the function 5 – x – 2x2 , and the corresponding value of x.

Solution:
$\begin{array}{l}5-x-2{x}^{2}\\ =-2{x}^{2}-x+5\\ =-2\left[{x}^{2}+\frac{1}{2}x-\frac{5}{2}\right]\\ =-2\left[{x}^{2}+\frac{1}{2}x+{\left(\frac{1}{4}\right)}^{2}-{\left(\frac{1}{4}\right)}^{2}-\frac{5}{2}\right]\\ =-2\left[{\left(x+\frac{1}{4}\right)}^{2}-\frac{1}{16}-\frac{5}{2}\right]\\ =-2\left[{\left(x+\frac{1}{4}\right)}^{2}-\frac{41}{16}\right]\\ =-2{\left(x+\frac{1}{4}\right)}^{2}+5\frac{1}{8}\end{array}$