Algebra II
Standard
|
| Skills (Note:
none listed for science standards)
|
Teacher
Strategy
|
Student
Tasks or Scientific Investigation/Experimentation
|
Assessment
or Scientific Application/Assessment
|
Resources
and Technology
|
|
The California Mathematics Content Standards -Grade8 9 10 11 12
Algebra II
Standard
17. Given a quadratic equation of the
form ax2 + by2 + cx + dy + e = 0,
students can use the method of
completing the square to put the
equation into standard form and can
recognize whether its graph is a
circle, ellipse, parabola, or
hyperbola. Students can then graph
the equation.
Skills (Note: none listed for science standards)
Teacher Strategy
Review completing the square method. Quadratic equations can be solved by taking the square root of each side.First the expression that contains the variable must be the square of a binomial.If this is not already the case,then you can make it so by using a process called Completing the Square You find half the coefficient of the linear term,square it,and add the result to each side.
Student Tasks or Scientific Investigation/Experimentation
Have students work on completing the square
method.Have them determine if the quadratic
equation is in the form of a circle,ellipse,
parabola or hyperbola.Give students an equation and have them put it
into standard form.Have students graph the
equation.Depending on their graph,ask them to
identify one of the following:If the graph is a parabola,identify its vertex.
If it ’s a circle,identify its center.
If it ’s an ellipse,identify its major/minor axes.
If it ’s a hyperbola,identify its asymptote.
Assessment or Scientific Application/Assessment
Give students representative graphs of circles,
parabolas,and ellipses not centered at the origin
and have them write their equations.Give students an equation that is not in standard
form and have them determine if the equation is
that of a circle,ellipse,parabola or hyperbola.
Resources and Technology
Resource:Algebra in the Real World,Dale Seymour Publications Technology:Algebra and Calculus Sketches by Ruth Carver at http://www.forum.swarthmore.edu/sum95/ruth/sketches/algcalc.html.Viewing sketches on this page requires The Geometer ’s Sketchpad.It has demo versions of the Sketchpad.
This page is taken from the Santa Clara Office of Education.