Name ________________________________ Date ____________________ Algebra I Review Factoring & Solving Quadratics Methods to Factor Quadratic Equations Completing The Square Factoring Trinomials Quadratic Formula !
!
! !
x2 + (a + b)x + (ab) à ax2 + bx + ! = c + ! Compare to ax2 + bx + c and (x + a)(x + b) substitute Now I can factor the trinomial as What multiplies to the third term explained in the first column, or and adds to the middle term? using the difference of two squares. I.) Match the following quadratics with their roots: _____ x2 + 10x + 11 a. x = -­‐11, 1 _____ x2 + 10x – 11 b. x = 3, 7 _____ x2 – 10x + 11 c. x = −5 ± 14 _____ x2 – 10x – 11 d. x = 5 ± 14 _____ (x -­‐ 5)2 = 4 e. x = 11, -­‐1 II. Solve by Factoring 1.) x2 – 64 = 0 2.) x2 – 6x – 16 = 0 3.) x2 + 3x = 40 4.) 2 x 2 + 3x + 1 = 0 5.) x² – 100 = 0 6.) x² + 6x = 0 III. Solve by using the quadratic formula: 7.) x² + 3x + 2 = 0 8.) 4x² – 8x = 1 IV. Solve each equation any way you want. Show your work. 10.) x2 + 11x + 18 = 0 11.) x2 + 2x + 1 = 15 13.) (x + 2)² = 36 14.) 3𝑥2−9𝑥 = −6 9.) x² + 8x = 0 12.) 7x2 – 9x +1 = 0 15.) x² – 6x + 2 = 0 16.) 3𝑥2 + 12𝑥 − 6 = 4x -­‐ 3
VI. REASONING: 18.) Explain why x² = -­‐81 DOES NOT have a solution. 17.) 2𝑥2 −5𝑥+2 = 0 19.) Which method can’t you use to solve this problem? x² – 47 = 0 Circle one: Factoring Square Roots Quadratic Formula Explain why: 20.) Which method can’t you use to solve this problem? x² + 7x = 0 Circle one: Factoring Square Roots Quadratic Formula Explain why: 21.) Which method can you use to solve all quadratic equations? Circle one: Factoring Square Roots Quadratic Formula Explain why: 22.) What are the two mistakes in setting up the quadratic formula: Solve: 2x² – x – 6 = 0 − 1 ± (−1) 2 − 4(2)(6)
x=
2(2)
23.) Solve this quadratic equation ALL three ways. Make sure you get the same answers! 𝑥 ! − 8𝑥 = 9 FACTORING COMPLETING THE SQUARE QUADRATIC FORMULA 24.) Use any method you’d like to solve. Remember, not all quadratics can be factored! 𝑥 ! + 4𝑥 − 8 = 0 𝑥 ! + 8𝑥 + 16 = 0 25.) y = 2x + 8x + 6
a) Describe the characteristics of each equation. b) Make a table of values and graph each function.
(6 extra points besides the vertex.)
c) State the domain and range.
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Family: ________________________________________ Form: ___Vertex or Standard (circle one)_ Direction: ________________________________________ Size: ________________________________________ Special point (specify): __________________________ AOS: ________________________________________ Domain: ________________________________________ Range: ________________________________________ Roots: __________________________________________ 26.) A punter kicked the football into the air with an upward velocity of
75 ft/s and at an initial height of 3 ft. The ball lands in the stands 15 ft
above the ground. What is the maximum height the ball reaches? How
long will it take the football to reach the maximum height? What is the
range of the function. How long does it take for the ball to hit the ground?