Algebra 1 | Unit 7 | Lesson 20: Rational and Irrational Solutions | Practice Problems

Decide whether each number is rational or irrational.

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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. \((x+1)^2 = 4\)

Solve each equation. Then, determine if the solutions are rational or irrational. \((x-5)^2 = 36\)

Solve each equation. Then, determine if the solutions are rational or irrational. \((x+3)^2 = 11\)

Solve each equation. Then, determine if the solutions are rational or irrational. \((x-4)^2 = 6\)

Based on the graph, what are the solutions to the equation \(81(x-3)^2 = 4\)? Can you tell whether they are rational or irrational? Explain how you know.

Match each equation to an equivalent equation with a perfect square on one side.

To derive the quadratic formula, we can multiply \(ax^2+bx+c=0\) by an expression so that the coefficient of \(x^2\) is a perfect square and the coefficient of \(x\) is an even number. Which expression, \(a\), \(2a\), or \(4a\), would you multiply \(ax^2+bx+c=0\) by to get started deriving the quadratic formula?

Here is a graph that represents \(y=x^2\). On the same coordinate plane, sketch and label the graph that represents each equation: \(y=\text-x^2-4\) and \(y=2x^2+4\).