# Test: Quadratic Function II - Ambitious

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Question 1:   Find the minimum or maximum value of ${x}^{2}+5x+17=0$
Maximum at $\left(1\frac{1}{2},6\frac{1}{4}\right)$
Minimum at $\left(-2\frac{1}{2},10\frac{3}{4}\right)$
Minimum at $\left(-2\frac{2}{3},7\frac{5}{8}\right)$
Maximum at $\left(-2\frac{1}{4},9\frac{2}{3}\right)$
Question 2:   Find the minimum or maximum value of $12-13x-3{x}^{2}=0$
Maximum at $\left(-2\frac{1}{3},23\frac{2}{5}\right)$
Maximum at $\left(-1\frac{5}{6},17\frac{1}{4}\right)$
Maximum at $\left(3\frac{1}{5},7\frac{4}{7}\right)$
Maximum at $\left(-2\frac{1}{6},26\frac{1}{12}\right)$
Question 3:   Solve the simultaneous equations: $\left\{\begin{array}{l}3y+3x=21\\ 2{y}^{2}-{x}^{2}=17\end{array}$
$\left\{\begin{array}{l}y=-12.42\\ x=19.42\end{array}$ or : $\left\{\begin{array}{l}y=3.759\\ x=3.241\end{array}$
$\left\{\begin{array}{l}y=-4.25\\ x=11.2\end{array}$ or : $\left\{\begin{array}{l}y=5.34\\ x=2.66\end{array}$
$\left\{\begin{array}{l}y=-17.723\\ x=24.723\end{array}$ or : $\left\{\begin{array}{l}y=3.723\\ x=3.277\end{array}$
$\left\{\begin{array}{l}y=-3\\ x=10\end{array}$ or : $\left\{\begin{array}{l}y=7\\ x=0\end{array}$
Question 4:   Solve the simultaneous equations: $\left\{\begin{array}{l}3x+y=5\\ {x}^{2}+{y}^{2}=13\end{array}$
$\left\{\begin{array}{l}x=0.475\\ y=3.575\end{array}$ or $\left\{\begin{array}{l}x=2.525\\ y=-2.575\end{array}$
$\left\{\begin{array}{l}x=0.45\\ y=1.705\end{array}$ or $\left\{\begin{array}{l}x=3.299\\ y=-5.175\end{array}$
$\left\{\begin{array}{l}x=1.755\\ y=8.935\end{array}$ or $\left\{\begin{array}{l}x=-1.365\\ y=-6.225\end{array}$
$\left\{\begin{array}{l}x=0.225\\ y=3.125\end{array}$ or $\left\{\begin{array}{l}x=0.315\\ y=4.095\end{array}$
Question 5:   If the roots of $3{x}^{2}-5x+2=0$ are ${x}_{1}$ and ${x}_{2}$, find the equation whith the roots ${x}_{1}^{2}+1$, ${x}_{2}^{2}+1$
$9{x}^{2}-16x+6=0$
$9{x}^{2}-31x+26=0$
$6{x}^{2}-17x+23=0$
$-3{x}^{2}+15x-5=0$
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