3. By rewriting \( f \) in the form \( f(x)=a(x-h)^{2}+k \), sketch the graph and find the domain and range of each of the following functions (a) \( f(x)=x^{2}-3 x-2 \) (b) \( f(x)=2 x^{2}-8 x+7 \) (c) \( f(x)=x^{2}-x-6 \)

Which of the following shows the equation \( 6^{2}=36 \) written in logarithmic form? (1 point) \( \log _{6} 36=2 \) \( \log _{2} 36=6 \) \( \log _{2} 6=36 \) \( \log _{36} 2=6 \)

determine whether the given quadratic function has a maximum or a minimum value and then find the value. \( y=-x^{2}+6 x-5 \) \( \begin{array}{lll}\text { [A] minimum, } 3 & \text { [B] minimum, } 4 & \text { [C] maximum, } 4\end{array} \quad \) [D] maximum, 3 A \( \begin{array}{ll}\text { B }\end{array} \) \( \begin{array}{l}\text { C }\end{array} \)

What function is the reflection of \( f(x)=|x+2| \) about the \( x \)-axis? \( g(x)=|x-2| \) Non of the other options \( g(x)=|-x+2| \) \( g(x)=-|x-2| \)

The half-life of radium is 1690 years. If 60 grams are present now, how much will be present in 430 years? \( \square \) grams (Do not round until the final answer. Then round to the nearest thousandth as needed.)

Julie swam, biked, and ran in a 22.2 mile triathlon. She completed the race in 2.15 hours. The function \( m=13.8 \mathrm{~h} \) represents the miles \( m \) Julie biked in \( h \) hours. Was her average speed biking less than or greater than her average speed for the entire race? Justify your answer. Round to the nearest tenth if necessary.