Question

How can you use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph and interpret these in terms of a context?

I've got the zeros part. The rest just... I'm not sure.

Answer 1

@jim_thompson5910

Answer 2

how would you complete the square on something like x^2 + 5x + 6 ?

Answer 3

I'm not really sure.

Answer 4

x^2 + 5x + 6 is the same as 1x^2 + 5x + 6

Answer 5

1x^2 + 5x + 6 is in the form ax^2 + bx + c

a = 1
b = 5
c = 6

Answer 6

plug a = 1 and b = 5 into h = -b/(2a) and tell me what you get for h

Answer 7

well
h = -5/(2 times 1)
h = -5 (2)
h = -10?

I'm not really great at stuff like that, which is why I'm basically not understanding any algebra.

Answer 8

it would be -5/2 = -2.5

Answer 9

mm, okay. I thought I'd learned that you'd multiply something like that, but okay.

Answer 10

so h = -2.5

Answer 11

we plug this into x^2 + 5x + 6 to find the value of k

Answer 12

k = h^2 + 5h + 6

k = (-2.5)^2 + 5(-2.5) + 6

k = -0.25

Answer 13

so we know this

a = 1 (given)
h = -2.5
k = -0.25

and we plug all that into y = a(x-h)^2 + k to get this

y = a(x-h)^2 + k
y = 1(x-(-2.5))^2 + (-0.25)
y = (x+2.5)^2 - 0.25

Answer 14

so y = x^2 + 5x + 6 turns into y = (x+2.5)^2 - 0.25 after we complete the square

Answer 15

what does completing the square get us? it tells us what the vertex and axis of symmetry are

vertex: (h,k) = (-2.5, -0.25)

axis of symmetry: x = h = -2.5