Question

Use the following quadratics and the questions below to prepare for the exploration meeting: a. y = x2 + 8x + 12 b. -(x + 3)2 - 6 = 0 c. y = (x+3)(x - 2) d. x2 – 3x + 3 = 0 e. f(x) = -0.35x2 - 4.65x + 1.75 f. x2 - 12x + 35 = 0 g. y = (x - 2.5)2 - 1.25 When you come to the exploration meeting, be ready to discuss the following: 1. What are some methods for calculating the vertex and axis of symmetry for each equation? 2. Determine which solution method you would prefer to use to solve each of the equations. What are the pros and cons of using that method for each situation? 3. In general, how would you decide which method is best for a given equation? 4. Without graphing each quadratic, what are some of the key features of the equation that will let you know what the graph will look like?

Answer 1

Solusion ca) y= x² + 8x + 12 converting this quachatic en in vertex form. y = (x² + 2x4x + 4) - 4+1 (x² + 2x4x +47) – 16+12 y = (x+4)² - 4 y = {x- (-4) ] ² - 4 g Comparing for year? tbx te go (x - 2)² + y Where (h, k) = vertex x=h- vertex form and line of symetry n=-4, k=a4 Here Vertex = (-4,-4) and love of syrnety x=-4 In this problems we have found vertex free by wenz vertex formy of quachetics 0 (b) -(x+3)2 - 6 - (x+3)2 +6=0 (x+37² 6=0 (2-(-3)) ?-6=0 This equation is already in vertex formy, ivertex = (1,k) - 63,-6). Anis on synety = x=-4 As

y = (x+3) G-2) for x intercept (x+3)(x-2) 20 x = -3, x=2 2 axis of symetry x + X₂ -342 2 axis of synty OCE -1/2 at x=tly; y = (-12 + 3) (2 2-2) = (-1/2) =(-0.5, -6.25 y Hence, Vertex -25 y d) x²-3n+3 = 0 at 22-34 +3=4 z =) *+-2-(3)2 +°)*+3-9 (x - 3j* – – +30 = (2-3)? + sy vestes 24) (05,008) | Axis of synnery x= 1.5 or 2 = 3/2 4 1, (e) fim 0.35x² – 4.650+ 1.75 Vertex is either minima er maxiona point for maxima & minima flanco differentiating the function on a equeting to

falz - 0.350² _ 4.65* + 1.75 t'a = -0.35 x 2a – 4.65 -0 - 0.70x 2 4-65 4.65 - 6.64 0.70 for at x = 6.64 Henu synny - 12 = -6.64 Let fo) = -0.35x66.647 - 4.65*66-64) +1.75 for = 17.19 vertex - 6-6-64, 1975) Axis og synty (f) x²- 12x +35=0 x² - 12x +35= +35-5 = 2?– 2x6x +62-62735 y = (x-6) ² - 36+35 (2-6) ² - 1 Vertex : (hk) (6,-1) Axis of synty [x=6 (8) y = (R-215)² - 1:25 y g Am -1.25 - This is already in vertex forn. where, = 2.5 ka - 1.25 [vertex (205, -1,25 and. Axis of synty synty TR = 2.3

vertex and % ☺ we have Calculated axis of symetry for given functicy By vertex Method By Root method atna By max/min diffentiae method we prefer vertex Forum evaluate the equation converted in vertex fom. for factor form of qualitic (-a) OC-b) - we will use Root nethod.) a interest metrod. for other form diforntial for Maxxl rain which is simply with ur aut is The key feature of equation (quadrctic) to decide the graph its leading Co-efficial y = ax² tbx te ayo Concave upward. u graph wil Concare clowanware n other, key point one Axis of symety and vertex axis of synly. graph will a co vertex N and other key post one x interupt when y so y intercept x=0 By knowing all the above ky posne, one can easily drow the graph of funtion.