Q-1: Given the quadratic function: f(x) = y = - x² -8x -15

(a) Use completing the square method to convert the given equation into the standard form of a parabola with vertical axis. Show all steps.

[Hint: The standard form is : y = a(x - h)² + k, a 0]

(b) Use the result of part (a) to find each of the following.

#1. Coordinates of the vertex

#2 The equation of the axis

#3. Direction in which parabola opens

#4. X- intercepts, if any

#5. Y-intercept

(c) Graph the parabola, showing all the relevant information on the graph

Reference: Example: y=f(x) = - 3x2 + 24x - 46 Step 1: y= (- 3x2 - 8x) - 46 Step 2: y= - 3(x2 - 8x) - 46 Step 3: y +( - 3)(-4)2 = - 3[ x2 - 8x + (-4)2 ]- 46 Step 4 : y - 48 = - 3( x - 4)2 -46 y = - 3(x- 4)2-46 + 48 a= -3, h= 4, k=2 Vertex (4,2) Axis: X=4 Opens: Down X-intercept: (4+V6/3,0), (4-V6/3,0) 0=-3(x-4)2 (x-4)2 = 2/3 x-4 = +V6/3,- V6/3 x=4 +V6/3,- V6/3 y-intercept (0,-46) domain (-00, 00) range (-0o, 2) Inc over (-00, 4) Dec over (4, 00)