Homework graph quadratic fuctions in standard form

Question

Graph the fuction by hand. Find the vertex round approximate coordinates to the second decimal place.

y=-3x^2+12x-7

Answer 1

3x^2 + 12x -17

take the derivative and set =0

y' = 6x +12 = 0

6x =-12

x =-12/6

x =-2 = x coordinate of the vertex

y coordinate = 3(-2)^2 + 12(-2) -7 = 12--24-7 =-19

vertex is (-2, -19)

3x^2 +12x - 7 = 0

= 3(x^2 +4x) -7 = 0

3(x^2 +4x + 4) = 7 +3(4) = 19

= 3(x+2)^2 =19 = y coordinate of the vertex

to find x intercepts divide by 3 and take the square root

(x+2)^2 = 19/3

x+2 = sqr(19/3)

x=-2 + or - sqr(19/3) = 0.5166 or -4.5166 = about 0.52 or -4.52

y intercept = the constant term = -7

plot the vertex and intercepts. put a parabolic shaped curve through them, axis of symmetry is x=-2