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Quadratics, SMB-006

  1. Complete the table of values for the equation  `y=2-x^2/2`.  (1 mark)

\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2 \ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} &   &  & 2 &  &  0 \\
\hline
\end{array}

  1. Sketch the graph  `y=2-x^2/2`  (2 marks)  
      

      
  2. For what range of `x`-values is the parabola concave up?  (1 mark)

Show Answers Only

i.   

\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2 \ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & 0  & \frac{3}{2} & 2 & \frac{3}{2} &  0 \\
\hline
\end{array}

ii. 

 

iii.   `text{The parabola is concave down for all values of}\ x.`

`=>\ text{There are no values of}\ x\ text{where the graph is concave up.}`

Show Worked Solution

i.   

\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2 \ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & 0  & \frac{3}{2} & 2 & \frac{3}{2} &  0 \\
\hline
\end{array}

ii. 

 

iii.   `text{The parabola is concave down for all values of}\ x.`

`=>\ text{There are no values of}\ x\ text{where the graph is concave up.}`

Quadratics, SMB-005

  1. Complete the table of values for the equation  `y=8-2x^2`.  (1 mark)

\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -3 & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \ & \ \ 3 \ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} &  &   & 6 &  &  &  & -10  \\
\hline
\end{array}

  1. Sketch the graph  `y=8-2x^2`  (2 marks) 
      
  2. For what range of `x`-values is the parabola concave down?  (1 mark)

Show Answers Only

i.   

\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -3 & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \ & \ \ 3 \ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & -10 & 0  & 6 & 8 & 6 & 0 & -10  \\
\hline
\end{array}

ii. 

 

iii.   `text{The parabola is concave down for all values of}\ x.`

Show Worked Solution

i.   

\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -3 & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \ & \ \ 3 \ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & -10 & 0  & 6 & 8 & 6 & 0 & -10  \\
\hline
\end{array}

ii. 

 

iii.   `text{The parabola is concave down for all values of}\ x.`

Quadratics, SMB-004

  1. Complete the table of values for the equation  `y=4-x^2`.  (1 mark)

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} &  &   &  & 3 &  \\
\hline
\end{array}

  1. Sketch the graph  `y=4-x^2`  (2 marks)  
      
  2. What are the coordinates of the vertex of the parabola?  (1 mark)

Show Answers Only

 

Show Worked Solution

i.   

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & 0 & 3  & 4 & 3 & 0 \\
\hline
\end{array}

ii. 

 

iii.   `text{Vertex at (0,4)}`

Quadratics, SMB-003

By completing the table of values, sketch the graph of  `y=2x^2-3`.  (3 marks)

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} &  &   &  & -1 &  \\
\hline
\end{array}


Show Answers Only

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & 5 & -1  & -3 & -1 & 5 \\
\hline
\end{array}

Show Worked Solution

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & 5 & -1  & -3 & -1 & 5 \\
\hline
\end{array}

Quadratics, SMB-002

By completing the table of values, sketch the graph of  `y=x^2+3`.  (3 marks)

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} &  &   &  & 4 &  \\
\hline
\end{array}


Show Answers Only

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & 7 & 4  & 3 & 4 & 7 \\
\hline
\end{array}

Show Worked Solution

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & 7 & 4  & 3 & 4 & 7 \\
\hline
\end{array}

Quadratics, SMB-001

By completing the table of values, sketch the graph of  `y=x^2-2`.  (3 marks)

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} &  & -1  &  &  &  \\
\hline
\end{array}


Show Answers Only

Show Worked Solution

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & 2 & -1  & 0 & -1 & 2 \\
\hline
\end{array}