University:
Missouri State University
Course:
MTH 103 | Intermediate Algebra
Academic year:

2019
Views:

105

Pages:

6
Author:

Bennett Wheeler

Algebra 2/Trig1 Graphing Quadratic Equations Name KEY Block Date (Linear Equation: equations with an exponent of one. Graphs are lines Standard Form y = mx + b Quadratic Equations: equations with an exponent of two (squared). Graphs are perabolas Standard Form y = a * x ^ 2 + bx + c (O-snaped) Opening up Opening down (flipped) positive a negative a Write the quadratic equation in standard form and determine if the graph opens up or down. 1.) y = 2x ^ 2 + x - 1 ק 2.) y = 3 - x - x ^ 2 j = - x ^ 2 - x - 3 3.) y = - 3x ^ 2 + 1 - 4x y= - 2x ^ 2 -4 ne+1 DOWN 4.) y = 4 - 3x ^ 2 y = - 3x ^ 2 + 4 5.) y = x + 9x ^ 2 f = 9x ^ 2 + x 6.) y = 3x ^ 2 + 5x ^ 2 - 3x + 2 y = 8x ^ 2 - 3x + 2 BAHATION = Vertex: the lowest or the highest point of the graph (end of -shepe) Axis of Symmetry: the vertical line through the vertex Axis of Symmetry and x-coordinate of the vertex x = - b/(2a) (- b)/(2a) d = 6x ^ 2 + bx + c of symmetry of the parabola. (7.) y = 2x ^ 2 + 4x - 1 2-1 8.) y = - x ^ 2 + 2x + 5 - 5/(2 - 1) = - 2/- 2 = 1 9.) y = 3x ^ 2 - 5 y = 3x ^ 2 + 0x - 5 x = (- Delta)/(2 - 3) = (- Delta)/6 = - c x= x= x = Find the vertex of the parabola. Find x using formula and then plug it back into equation to find y. (10.) y = x ^ 2 + 2x - 1 11.) y = - x ^ 2 + 4 y = - x ^ 2 + 0 = 4 x = - b/(2C) = - zeta_{0}/(2C) = zeta_{0}/(2C) = zeta_{0} f = - (a) ^ 2 + 4 y - 4 (0.4) ۱-20 y = (- 1) ^ 2 * 2(- 1) - 1 q = 1 - 2 - 1 1 ^ 2 - 2 (12) 12.) y = 2x ^ 2 + 4x x= - d/(2 * 2) = 4/4 * z - 1 y = 2 * (- 1) ^ 2 + 4(n) \\ =2-4 aligned q' = 2 - 4 - (- 1, - 2) Graph the following quadratic equations. Find the axis of symmetry and the vertex. 13. y = x ^ 2 - 2x + 3 x Vertex: (1,2) Point: (0,3) () (2,3) y = x ^ 2 + 5x - 6 x = - 2.5 Vertex: (-25, -12.25) Point: (0, - c_{2}) ((1,0) 15. y = - x ^ 2 + 4x - 2 x = Z Vertex: (2,2) Point (0, - 2) (1.1) Standard Form: Practice Problems: pg 253 #20-25 17-19 17C 18A 115 20.) y = x ^ 2 - 2x - 1 x= 21.) y = 2x ^ 2 - 12x + 19 x = 3 22.) y = - x ^ 2 + 4x - 2 x = 2 Vertex: (6, - 2) Vertex: (3,1) Point: (2,3) (4.3) Vertex: (2,2) Point: (01) (2,-1) Point: ( phi_{i} -2.) 23.) y = - 3x ^ 2 + 5 x = underline \ 0 Vertex: (0,5) Point: (1, 2)(- 1, 2) 24.) y = 1/2 * x ^ 2 + 4x + 5 x = - 4 Vertex: (-4,-3) Point: (-3,-2.5) (- \mathfrak{s}, - 2, xi) 25) y = 1/6 / 6 * x ^ 2 - x - 3 x = - 3 Vertex: (- 3, - 1, 5) Point: (- 4, (- 1 ^ 2) / 3) (- 2, - 1 2/3)