Question

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- -**+- 2 -(x + 2) + 1 21. f) 30. FOX) -- М. 31. g) 3 32 g(x) = 2x2 + 4x + 3 33. g(x) = -2x + 8x - 3 34. g(x) = -3x + 6x For each of the following equations, find the coordinates of the vertex, and indicate whether the vertex is the highest point on the graph or the lowest point on the graph. (Do not graph.) 35. f(x) = x2 - 6x + 5 36. f(x) = -x + 6x - 5 37. f(x) = -x + 2x + 8 38. f(x) = x - 2x - 8 41. f(x) = -r- 8x 42. Rx) = x + Bx 39. f(x) = 12 + 4x - 40. f(x) = -12 - 4x + x

I need help with 30,33,35,36,37,38
the instructions for 30 and 33 are. find the vertex and any two convenient points to sketch the graph of the follwing functions

Answer 1

3 - -4 -3 -2 1 2 3 45 (6,-2) 3 33) g(x) - - 201² + 8x-3 a= -2 b=8 e = -3 oc coordinate of vertex -b 2a = 2 - (88) 2X(-2) y coordinate of vertex -2(2)² + 8(2)=3 = 5 Vertex (2,5) o intercept (when y=0) O=-2x² +88-3 2x²-80+3=0 x = -(-8) + J (8)² - 4x2x3 n 2 x 2 8 I HO 니 47 Vio 2

intercept . u tvio, 0) (4.-10,0) 5 4 3 - 2 - (HATTO ,o) 1 - Joop! 1 2 3 5 35) fex) = x2-6x +5 a = 1 b = -6 c=5 o coordinate of vertex -b 2a -(-6) 3 2X I y Coordinate of vertex = (3) ² - 6(3) +5 --4 vertex = (3,-4) As a is the the function will be upward concave So verdex is the lowest point 36) fel) = sc² +6x-s b = 6 a coordinate of vertex 2x-1) a = -1 c = -5 - b 2a - 6 = 3

y Coordinate of vertex = (3) + 6(3) - 5 - 4 vertex = (3,4) As a is-ve the function graph with be downward Concave, so vertex is highest point foc) = -x² 37) + 2x + 8 a = -1 b=2 c=8 x coordinate of vertex = -b za z -2 2-1) y coordinade of vertex = -(1)² + 2(1) +8 a As a is - ve vertes=(1,9) the function graph will be Concave downward, so verdex is highest point foc) = -x-20-8 a = -1 b= -2 c = -8 x Coordinate of vertex = -b za =-(-2) 2x(-) = -1

y coordinate of vertes - (-1² - 2(-1)-8 - 1+2-8 - = - 7 vertex = (-1,-1) As a is-ve the function graph will be concave downward so vertex is highest point.