2021 Final Review for Quadratics Test (PDF)

More practice problems Date:_________________________ KEY NOTES/TOPICS FOR QUADRATICS TEST Factoring Solve by… o Factoring o Square Roots o Quadratic Formula o Completing t...

More practice problems Date:_________________________ KEY NOTES/TOPICS FOR QUADRATICS TEST Factoring Solve by… o Factoring o Square Roots o Quadratic Formula o Completing the Square Simplify square roots Complex Numbers (simplify/solve) Graphing from vertex form, standard form, or factored form o Know how to convert when necessary o Label/State – Vertex, axis of symmetry, y-intercepts, x-intercepts § If no x-intercepts, state a symmetric point Write the equations of a parabola given certain information Finding the axis of symmetry, max or min values, domain or range Discriminant and what it means for a function/equation 1. Graph f (x) = −3(x + 2)(x − 4) without converting 2. Find the discriminant and state what it means to vertex form. State all necessary info. for f (x) = 2x 2 + 6x + 7 3. What is the equation of the axis of symmetry for y = 3x 2 − 4x + 2 ? # 4. Determine if 𝑦 = $ 𝑥 $ − 5𝑥 + 3 has a max or a min. Find the max or min value and state the domain and range. 5. Write the equation of the parabola with vertex (-2, -5) and containing the point (4, -3). $ 6. Write the equation of the parabola in vertex form that has an axis of symmetry of x = * and passes through the points (-1, 3) and (0, 2). # 7. Convert 𝑦 = $ 𝑥 $ + 3𝑥 − 4 to vertex form by completing the square, then graph as we did in class. 8. Write the standard form equation of the parabola with x-intercepts of 3 and -1 that passes through the point (-2, 10). 9. Factor the following: a. 25𝑦 $ − 9𝑎$ + 12𝑎𝑏 − 4𝑏$ b. 6(𝑥 + 2)$ − 11(𝑥 + 2) − 10 c. 𝑥 5 − 64 d. r 2 + t 2 - 4m 2 + 4m - 1 - 2rt e. 6𝑥 67 + 28𝑥 $7 − 10 10. Solve over C using the most efficient methods: 3 2 2 a. 12x 2 = x 4 - x 3 b. 3 x 2 - = ( x + 5) 4 3 # c. * (2𝑥 + 1)$ + 4 = 0 d. 3𝑥 $ + 7𝑥 = 9 e. ( 5 - x ) = 2 ( x - 5 ) 2 f. −𝑥 $ + 4𝑥 = 12 g. ( a + 3b ) - ( 3a - b ) i = 6 - i (note: a and b are real numbers) 11. Simplify completely using most efficient methods: æ x5 y 4 ö a. ( ) 6 x3 y -4 ç ç 18 è ÷ ÷ ø æ 2 - 4i ö æ 3i ö b. ç ÷×ç ÷ è 1 + 3i ø è 2 - 6i ø 3i 3i c. -32x -4 y -1 d. - 2+i 2-i æ -12 x3 y -2 öæ -8 ö e. ç ÷ çç ÷÷ ç 18 ÷ 6 x5 y -3 è øè ø ANSWERS 1. V(1, 27); aos x=1; y-int (0, 24) sym pt (2, 24) ; x-int (-2, 0) and (4, 0) 2. D = -20; no x-intercepts 3. x = 2/3 4. min value of -19/2 #A * Do only using h=-b/2a! D: {𝑥|ℝ}, R: >𝑦?𝑦 ≥ − $ B 2 1 3æ 2 ö 38 5. y = (x + 2)2 − 5 6. y = ç x - ÷ + 18 7è 3 ø 21 # #C 7. 𝑦 = $ (𝑥 + 3)$ − $ ; V(-3, -17/2), AOS: x=-3, y-int: (0, -4) sym pt (-6,-4), x-int: exact (−3 ± √17, 0), approx. (1.12,0)(-7.12,0) 8. 𝑦 = 2𝑥 $ − 4𝑥 − 6 (be sure to start with factored form) 9. a. (5𝑦 − 3𝑎 + 2𝑏)(5𝑦 + 3𝑎 − 2𝑏) b. (3𝑥 + 8)(2𝑥 − 1) c. (𝑥 − 2)(𝑥 $ + 2𝑥 + 4)(𝑥 + 2)(𝑥 $ − 2𝑥 + 4) d. (𝑟 − 𝑡 − 2𝑚 + 1)(𝑟 − 𝑡 + 2𝑚 − 1) e. 2(3𝑥 $7 − 1)(𝑥 $7 + 5) b. 𝑥 = ± √7L2 M#±$N√* 10. a. 𝑥 = 0𝐷𝑅, 4, −3 c. 𝑥 = $ MC±√#OC d. 𝑥 = 5 e. 𝑥 = 5, 7 f. 𝑥 = 2 ± 2𝑖√2 A #C g. 𝑎 = #Q , 𝑏 = #Q R S √* 5T*N 6N U$V 5 M$U$V 11. a. * b. #Q c. R WV d. O e. *R