While working in our polynomials unit, a page had some review problems.
Students where given equations similar to:
And asked to solve.
I changed the directions… to graph the expression in Y= and record the x-intercepts.
Then look for connections between the intercepts and given equations.
Some nice conversations took place.
After a discussion/sharing, there was some confusion about signs being different from the expressions. We talked about the location of the intercepts, sharing how we could create factors…which connected back to translations.
Some students shared how to tell if intercepts were on same side of origin or one positive, one negative.
Others shared – if they substituted the x-intercepts back into the equation, the result was zero.
And finally, someone shared how when they looked at the coordinates of x-intercepts (x,0) the y-value was =0. Bingo. Connecting to the functions zeroes.
So, I asked…what happens when we’re given this x(x^2+5x+6)=0?
Their thinking and reasoning can show through… I just need to get out of the way.
the radical rational... 