IM Alg1.7.5 Practice: How Many Solutions?
Rewrite each equation so that the expression on one side could be graphed and the x-intercepts of the graph would show the solutions to the equation.
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Determine how many solutions each , , and has. Explain how you know.
Mai is solving the equation . She writes that the solutions are and . Han looks at her work and disagrees. He says that only is a solution. Who do you agree with? Explain your reasoning.
The graph shows the number of square meters, , covered by algae in a lake weeks after it was first measured.
In a second lake, the number of square meters, , covered by algae is defined by the equation , where is the number of weeks since it was first measured.
For which algae population is the area decreasing more rapidly? Explain how you know.
If the equation is true, which is also true according to the zero product property?
Solve the equation .
Show that your solution or solutions are correct.
To solve the quadratic equation , Andre and Clare wrote the following:
Identify the mistake each student made.
Andre Clare
Solve the equation and show your reasoning.
Decide if each equation has 0, 1, or 2 solutions and explain how you know.