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Quadratic Equations Practice Worksheet 9.1

Practice solving quadratic equations using square roots, simplifying radical expressions, and completing the square. Understand square roots, perfect squares, and irrational numbers. Examples and practice problems included.

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Quadratic Equations Practice Worksheet 9.1

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  1. Do Now 4/29/19 • Take out CW/HW from last week. • Practiceworksheet 9.1 • Copy HW in your planner. • Text p. 501, #4-32 evens • Quiz Wednesday, Sections 9.1 & 9.3 A= 36 What is the area for each figure? A = 6² A= 16 A = 4² • What are the dimensions for each figure? 6 • Write an equation for area of the figure. 4 • Can you think of an equation for ONE side of the figure? 4 6

  2. Practice worksheet 9.1

  3. Practice worksheet 9.1

  4. Chapter 9 “Solving Quadratic Equations” • (9.1)Simplifying Radical Expressions • (9.3)Solving Quadratic Equations Using Square Roots • (9.4) Solving Quadratic Equations by Completing the Square • (9.5) Solving Quadratic Equations Using the Quadratic Formula • (9.6) Solving Nonlinear Systems of Equations

  5. Learning Goal SWBAT solve quadratic equations Learning Target SWBAT solve quadratic equations using square roots. 

  6. Remember This??? Section 6.2 “Radical & Rational Exponents” If b² = a then b is the square root of a. TheSQUARE ROOTof a number is denoted by the symbol , which is called aradical. radicand

  7. Remember This??? Square Roots • All positive real numbers have two square roots, a positive and negative square root. • The symbol is read as “plus or minus” and refers to both the positive and negative square root. • Negative real numbers do not have real square roots. So there is no solution. no solution The square of an integer is called a perfect square.

  8. Remember This??? Not PERFECT??? The square root of a whole number that is NOT a perfect square is an IRRATIONAL NUMBER. numbers that cannot be written as a quotient (fraction, ratio) of two integers and the decimal neither terminates nor repeats. To find the square root of a number that is not a perfect square estimate or use a calculator to find the square root.

  9. Section 9.3 “Solving Quadratic Equations Using Square Roots” • To use square roots to solve a quadratic equation of the form ax² + bx + c = 0, first isolate x² on one side of the equation to obtain x² = d. Examples Solving x² = d by Taking Square Roots - If d > 0, then x² = d has two solutions: - If d = 0, then x² = d has one solution: - If d < 0, then x² = d has no solution: no solution no solution

  10. Try It Out… No solution

  11. Take square roots of a fraction • In cases where you need to take the square root of a fraction whose numerator and denominator are perfect squares, the radical can be written as a fraction. • For example, can be written as .

  12. Try It Out…

  13. Solve the quadratic equation. Round your answer to the nearest hundredth.

  14. A touch tank has a height of 3 feet. Its length is three times its width. The volume of the tank is 270 ft.³. Find the length and width of the tank.

  15. HomeworkText p. 501, #4-32 evens

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