Answer:
Step-by-step explanation:
a)
y=2(x + 3)^2-1
this equation is in vertex form,
it is:
vertically stretched by a factor of 2
left 3 units (f(x)=a*(x - h)^(2)+k, so if h is positive it was -(-h) before ot got simplified)
down 1 unit
thus, vertex is (-3,-1)
b)
you can change it to standard form (f(x)=ax^(2)+bx+c) by:
simply multiplying everything out:
y=2(x + 3)^2-1
y=2(x^(2)+6x+9)-1
y=2x^(2)+12x+18-1
y=2x^(2)+12x+17
c)
y=x^2+16+2
this equation is in standard form ,
you can change it to vertex form (f(x)=a*(x - h)^(2)+k by:
y=1(x-h)^2+k
h=-b/2a
h=-16/2(1)
h=-8
solve for k
y=x^2+16+2
since vertex is (h,k) lets plug in h for x to find k and just solve for y:
k=y=(-8)^2+16+2
k=y=64+16+2
k=y=82
k=82
now that we know the vertex, lets write the equation in vertex form:
y=a*(x - h)^(2)+k
y=1(x-(-8))^(2)+82
y=(x+8)^2+82
