vertex form (2x+3)^2

Question

give the properties of the following?

(3-x) (2x+5)

Answer 1

y=(2x+3)²=4x²+12x+9=4(x²+3x+9/4)=4(x+3/2)², which is vertex form, with vertex at (-3/2,0).

y=(3-x)(2x+5)=6x+15-2x²-5x=-2x²+x+15,

y=-2(x²-x/2-15/2)=-2(x²-x/2+1/16-1/16-15/2),

y=-2(x-¼)²+1/8+15=-2(x-¼)²+121/8.

PROPERTIES

y-121/8=-2(x-¼)² is in vertex form so vertex is (¼,121/8). The lead coefficient -2 is negative, showing this parabola to be an inverted U shape so the vertex is the maximum. The axis of symmetry is x=¼. The x-intercepts are 3 and -5/2 (from the given factors) and the y-intercept is 15.