Write a quadratic function in standard form whose graph is shown.

Question

(-2,0) (4,-3) (6,0)

Answer 1

(-2,0,(4,-3),(6,0)

vertex has an x value midway between the x intercepts = (-2+6)/2 =4/2= 2

y =a(x-2)^2 + k

-3 =4a +k

-3 =1+k

k = -4

y = (1/4)(x-2)^2 -4 vertex = (2,-4) = minimum point

in y=a(x-h)^2 +k vertex form (h,k) = vertex = (2,-4)

y = a(x+2)(x-6)

-3 = a(6)(-2) = -12a

a = -3/-12 = 1/4

y = (1/4)(x^2-4x -12) = .25x^2 -x -3

in standard form y=ax^2 +bx +c with a=1/4=.25, b=-1, c=-3

Answer 2

y = a(x +2)(x - 6); - 3 = a(4 + 2)(4 - 6); - 3 = - 12a; a = 1/4; y = 1/4(x² - 4x - 12); y = 1/4x² - x - 3