Quadratic Equations, Inequalities and Modulus Functions
Question 1
Explain why the equation $\sqrt{{{x}^{2}}+3x+7}+\sqrt{{{x}^{2}}+3x-9}=2$ has no real roots.
Question 2
(a)
Find the value of $a$ and of $b$ for which $\left\{ x:-\frac{2}{3}<x<1 \right\}$ is the solution set of $3{{x}^{2}}+ax<b$.
[3]
(b)
Find the range of values of $m$ for which the curve $y=m{{x}^{2}}+4m-2$ does not intersect the line $y=3mx$ where $m$ is a constant.
[4]
(b) 
Question 3
2017 SNGS EOY Q3
The equation of a curve is $y=\left( k-6 \right){{x}^{2}}-8x+k$ , where $k$ is a constant. Find the range of values of $k$ for which the curve lies completely above the $x$-axis.
[5]
Question 4
Find the range of values of $p$ for which the curve $y={{x}^{2}}+{{\left( px+5 \right)}^{2}}-16$ is always above the $x-$axis for all real values of $x$.
Question 5
Solve $6{{\left| {{x}^{2}}-1 \right|}^{2}}-13\left| {{x}^{2}}-1 \right|=-2$.
Question 6
Given that $\left| {{a}^{2}}-{{b}^{2}} \right|=16$, ${{\left( a+b \right)}^{2}}=64$, find the value of $\left| {{\left( \frac{3a-3b}{a+b} \right)}^{4}} \right|$.
Question 7
Sketch the graph of each of the following, indicating any coordinates of the axial intercepts and asymptotes.
(a)
$y=\left| 6{{x}^{2}}-x-12 \right|$
(b)
$y=\left| {{e}^{2x}}-3 \right|$
(a)
(b)
