91Ó°ÊÓ

Simplify by using the imaginary unit \(i\). $$ \sqrt{-11} $$

Find an equation that shifts the graph of \(f\) by the desired amounts. Do not simplify. Graph \(f\) and the shifted graph in the same \(xy\)-plane. \(f(x)=x^{2} ;\) right 2 units, downward 3 units

Exercises \(1-28:\) Solve the quadratic equation. Check your answers for Exercises \(1-12\). $$ 9 x^{2}-11=0 $$

Simplify by using the imaginary unit \(i\). $$ \sqrt{-18} \cdot \sqrt{-2} $$

Write a formula for a function \(g\) whose graph is similar to \(f(x)\) but satisfies the given conditions. Do not simplify the formula. \(f(x)=\sqrt{x}\) (a) Reflected about the \(x\) -axis, shifted left 2 units (b) Reflected about the \(y\) -axis, shifted right 3 units

Write an equation that shifts the given circle in the specified manner. State the center and radius of the translated circle. \(x^{2}+y^{2}=7 ;\) left 3 units, downward 7 units

Write the expression in standard form. $$ (7+i)-(-8+5 i) $$

Solve the inequality. $$ x^{2}-3 x-10<0 $$

Solve each quadratic equation (a) graphically, (b) numerically, and (c) symbolically. Express graphical and numerical solutions to the nearest tenth when appropriate. $$ x^{2}-4=0 $$

Use transformations to explain how the graph of \(f\) can be found by using the graph of \(y=x^{2}\) \(y=\sqrt{x},\) or \(y=|x| .\) You do not need to graph \(y=f(x)\). \(f(x)=2(x-4)^{2}\)