University:
Williams College
Course:
MATH 102 | Foundations in Quantitative Skills
Academic year:

2021
Views:

115

Pages:

6
Author:

Hayley Stanton

Algebra 2 CP Chapter 4 Name: Key Test Review Assignment GRAPHING QUADRATICS - Know the following! Standard Form (y=ax^{2}+bx+c) Axis of Symmetry (x=-b/_{2}a) Vertex Plug in x-value of vertex to solve for y Max/Min y-value of vertex y-intercept ((0,c)) Vertex Form (y=a(x-h)^{2}+k) Axis of Symmetry (x=h) Vertex ((h,k)) Max/Min k value a max a min Shifts Find the following pieces of information: a) Axis of Symmetry, b) Vertex, c) Max or Min and Value, d) y-intercept, e) Create a Table, f) Graph (y=-2x^{2}-4x+3) (y=x^{2}-3) Find the following pieces of information: a) Axis of Symmetry, b) Vertex, c) Max or Min and Value, d) Create a Table, f) Graph (y=(x-3)^{2}) (y=-(x+3)^{2}+5) 5. (y=2(x+1)^{2}-3) a. (x=-1) b. ((-1,-3)) c. Min -3 [Graph of the quadratic function (y=2(x+1)^{2}-3)] 6. (y-4=\frac{1}{2}(x-1)^{2}) a. (x=1) b. ((1,4)) c. Min 4 [Graph of the quadratic function (y-4=\frac{1}{2}(x-1)^{2})] Graph the following inequalities: 7. (y>7x^{2}) [Graph of the inequality (y>7x^{2})] 8. (y\le-x^{2}+4x) [Graph of the inequality (y\le-x^{2}+4x)] 9. (y\ge x^{2}-4x+9) [Graph of the inequality (y\ge x^{2}-4x+9)] Graph the system of inequalities. Remember to shade in your final answer. 10. (\begin{cases}y\ge x^{2}-9\ y\le-x^{2}+4x+4\end{cases}) [Graph of the system of inequalities (y\ge x^{2}-9) and (y\le-x^{2}+4x+4)] 11. (\begin{cases}y-x^{2}+6\end{cases}) [Graph of the system of inequalities (y-x^{2}+6)] Methods for Solving Quadratic Equations Set = to zero and Factor Use the T Property: Isolate Whatever is being Squared Complete the Square Quadratic Formula Solve the following Quadratic Equations. Use the BEST method. (x^{2}+13x+40=0) ((x+5)(x+8)=0) (x=-5,-8) (x^{2}+42=17x) (x^{2}-17x+42=0) ((x-14)(x-3)=0) (x=14,3) (-126=3x^{2}) (3x^{2}+126=0) (3(x^{2}+42)=0) (3(x+7)(x-6)=0) (x=-7,6) (2x^{2}+5x+3=0) ((2x+3)(x+1)=0) (x=-3/_{2},-1) (4w^{2}-6w+2=0) (2(2w^{2}-3w+1)) (2(2w-1)(w-1)) (w=\frac{1}{2},1) (x^{2}=225) (x=\pm15) (x^{2}+7x+\frac{49}{4}=4) ((x+\frac{7}{2})^{2}=4) (x+\frac{7}{2}=2) (x=\frac{-3}{2}) (x+\frac{7}{2}=-2) (x=-\frac{11}{2}) (9x^{2}+30x+25=11) ((3x+5)^{2}=11) (3x+5=\pm\sqrt{11}) (3x=-5\pm\sqrt{11}) (x=\frac{-5\pm\sqrt{11}}{3}) (3x^{2}+12x=18) (3(x^{2}+4x-6)=0) (x^{2}+4x-6=0) (x^{2}+4x+4=10) ((x+2)^{2}=10) (x=-2\pm\sqrt{10}) (2x^{2}-3x-3=0) (x=\frac{3\pm\sqrt{33}}{4}) (x^{2}-\frac{5}{2}x-\frac{25}{16}=0) ((x-\frac{5}{4})^{2}=0) (x=\frac{5}{4}) (2x^{2}+8x+14=0) (2(x^{2}+4x+7)=0) (x=\frac{-4\pm2i\sqrt{3}}{2}) (x=-2\pm i\sqrt{3})