91Ó°ÊÓ

Solve by completing the square. Show your work. $$ t^{2}+8 t-3=0 $$

Explain why there are not two different solutions when the discriminant is \(0 .\)

Graph. \(2(y-7)=y-10\)

Number of Handshakes. There are \(n\) people in a room. The number \(N\) of possible handshakes by the people is given by the function $$N(n)=\frac{n(n-1)}{2}$$ For what number of people \(n\) is \(66 \leq N \leq 300 ?\)

Write an equation for a function having a graph with the same shape as the graph of \(f(x)=\frac{3}{5} x^{2},\) but with the given point as the vertex. $$ (4,-7) $$

Write the equation of the parabola that has the shape of \(f(x)=2 x^{2}\) or \(g(x)=-2 x^{2}\) and has a maximum value or a minimum value at the specified point. $$ \text { Minimum: }(-4,0) $$

Factor completely. $$ 3 y^{3}-300 y $$

Factor completely. $$ 20 x^{2}+7 x-6 $$