college algebra word problems

Question

Use the vertex (h, k)

 and a point on the graph (x, y)

 to find the general form of the equation of the quadratic function.

(h, k) = (−5, −1),    (x, y) = (−8, 8)

Answer 1

y = k(x+5)^2-1

8 = k(-8+5)^2 - 1

8 = k(-3)^2 - 1

8 = 9k - 1

9 = 9k

k=1

y = (x+5)^2 - 1 = x^2 + 10x + 25-1

= x^2 + 10x + 24

= (x+6)(x+4)

Note that upon completing hte square:

x^2+10x+24 = x^2 +10x+ 25 -25+24

(x+5)^2 -1