IM Alg1.7.20 Practice: Rational and Irrational Solutions
Decide whether each number is rational or irrational.
Here are the solutions to some quadratic equations.
Select all solutions that are rational.
Solve each equation. Then, determine if the solutions are rational or irrational.
Here is a graph of the equation .
Based on the graph, what are the solutions to the equation ?
Can you tell whether they are rational or irrational? Explain how you know.
Solve the equation using a different method and say whether the solutions are rational or irrational. Explain or show your reasoning.
Match each equation to an equivalent equation with a perfect square on one side.
To derive the quadratic formula, we can multiply by an expression so that the coefficient of a perfect square and the coefficient of an even number. Which expression, , , or , would you multiply by to get started deriving the quadratic formula?
What does the equation look like when you multiply both sides by your answer?
Here is a graph the represents y=x².
Which quadratic expression is in vertex form?
Function is defined by the expression . Evaluate .
Explain why is undefined.
Give a possible domain for .