Question

Determine the vertex of the function f(x)=2(x+1)(x+7). You must show all algebraic steps for full marks

Answer 1

vertex (-4,-18)

Explanation:

f(x)=2(x+1)(x+7)

f(x)=2(x^2+8x+7)

f(x)=2x^2+16x+14

f(x)=2(x^2+8x)+14

f(x)=2(x^2+8x+4^2-4^2)+14

f(x)=2(x^2+8x+4^2)+2(-4^2)+14

f(x)=2(x^2+8x+4^2)+2(-4^2)+14

f(x)=2(x^2+8x+4^2)-18

f(x)=2(x+4)^2-18

vertex form:

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

h=-4

k=-18

vertex (-4,-18)