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9-12 Integrated Math 2 Unit 5 Lesson 15

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Unit 5, Lesson 15

Quadratic Equations with Irrational Solutions

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Integrated Math 2

Practice

Problem 1

Solve each equation, and write the solutions using \(\pm\) notation.

\(x^2 = 144\)
\(x^2 = 5\)
\(4x^2 = 28\)
\(x^2 = \frac{25}{4}\)
\(2x^2 = 22\)
\(7x^2 = 16\)

Problem 2

Match each expression to an equivalent expression.

\(4 \pm 1\)
\(10 \pm \sqrt4\)
\(\text- 6 \pm 11\)
\(4 \pm \sqrt{10}\)
\(\sqrt{16} \pm \sqrt2\)

-17 and 5
\(4 + \sqrt2\) and \(4 - \sqrt2\)

8 and 12

3 and 5

\(4 + \sqrt10\) and \(4 - \sqrt{10}\)

Problem 3

Is \(\sqrt{4}\) a positive or negative number? Explain your reasoning.
Is \(\sqrt{5}\) a positive or negative number? Explain your reasoning.
Explain the difference between \(\sqrt{9}\) and the solutions to \(x^2 = 9\).

Problem 4

Technology required. For each equation, find the exact solutions by completing the square and the approximate solutions by graphing. Then, verify that the solutions found using the two methods are close.

\(x^2+10x+8=0\)

\(x^2-4x-11=0\)

Problem 5

ForLesson 10: Rewriting Quadratic Expressions in Factored Form (Part 4)

Which expression in factored form is equivalent to \(30x^2 +31x+5\)?

\((6x+5)(5x+1)\)
\((5x+5)(6x+1)\)
\((10x+5)(3x+1)\)
\((30x+5)(x+1)\)

Problem 6

ForLesson 6: Building Quadratic Functions to Describe Situations (Part 2)

Two rocks are launched straight up in the air. The height of Rock A is given by the function \(f\), where \(f(t) = 4 + 30t - 16t^2\). The height of Rock B is given by \(g\), where \(g(t) = 5 +20t - 16t^2\). In both functions, \(t\) is time measured in seconds after the rocks are launched, and height is measured in feet above the ground.

Which rock is launched from a higher point?
Which rock is launched with a greater velocity?