The equation of the quadratic function satisfying the given

The equation of the quadratic function satisfying the given conditions is P(x) =

Find the equation of the quadratic function satisfying the given conditions. The equation of the quadratic function satisfying the given conditions is P(x) = .

Solution

p(x) = a(x-h)^2 + k

vertex = (-3,-2)

(6,160 )

plugging the values of a,k and point in the given equation of p(x)

160 = a( 6-(-3))^2 - 2

160 = 81a - 2

162 = 81 a

a = 162 / 81

a = 2

hence , equation becomes

p(x) = 2(x+3)^2 - 2

p(x) = 2(x^2+9 + 6x) - 2

p(x) = 2x^2 +12x +16