Answer:
y=3(x-2)²+49
Explanation:
vertex-form is given as y=a(x-h)²+k, where (h,k) is the coordinate of the vertex
we are given the function in standard form, which is:
y=ax²+bx+c
our function is:
3x²-12x+61
the value of a is given as the value of the coefficient in front of the squared term (in this case, it's 3)
here's the function so far in vertex form:
y=3(x-h)²-k
now, we need to find the vertex
to find h, we can use the formula (-b/2a)
the value of b is given as the value of the coefficient in front of the linear term (in this case, it's -12)
and we know from above that a=3
substitute what we know into the formula:
h=-b/2a
h=12/2(3)
h=12/6
h=2
so h is 2
*Please note that when we substitute it into the function, it's -2
so here is our function so far:
y=3(x-2)²-k
now to find k, which is given in the formula c-(b²/4a)
we know from above that a=3, b=-12
c is the value of the constant (term without a variable). In this case, it's 61
once again, substitute what we know into the equation:
k=61-((-12)²/4(3))
k=61-(144/12)
k=61-12
k=49
therefore the function will be:
y=3(x-2)²+49
Hope this helps!