Question

What is the equation, in vertex form, of the quadratic function that has a vertex at V(-5, -4) and passes through point P(1, 8)?

Answer 1

In vertex form
y=a(x-h)²+k
(h,k) is the vertex
and a is some constant

given that the vertex is (-5,-4)
h=-5, k=-4
y=a(x-(-5))²+(-4)
y=a(x+5)²-4
find a by subsituting the gven point

(1,8)
when x=1, y=8

y=a(x+5)²-4
8=a(1+5)²-4
8=a(6)²-4
8=36a-4
add 4 to both sides
12=36a
divide both sides by 36
1/3=a

so the equation is
$y=\frac{1}{3}(x+5)^2-4$

that is the first option