given y=x^2 + bx + c vertex (-3,-5) find missing information for coefficient

Question

Algebra 2 in general is just ummm no. Please help asap, and thanks in advance.

Answer 1

a=1 is given

Vertex at x=-3 is given

-b/(2a) = -3

b/(2a) = 3

b = 6a = 6(1) = 6

y = x^2 + 6x + c is the quadratic function

(-3,-5) ---> -5 = (-3)^2 + 6(-3) + c

-5 = 9 - 18 + c

-5 = -9 + c

c = 4

The quadratic function is y = x^2 + 6x + 4

CHECK

= x^2 + 6x + 9 -9 + 4 <--- completes the square

= (x+3)^2 - 5 ---> (-3, -5) is the vertex