Question

find the vertex

Answer 1

The equation is written as \(y=ax^2+bx+c\)

You can find the x value of the vertex by doing \(x=\dfrac{-b}{2a}\) (The letters you can reference from the general equation I just wrote above)

Once you have x you can substitute back into the original equation to find the y value

Answer 2

so
b=−2xa
b=−2ya

Answer 3

Hmm you just have to substitute and solve for x

a = 1
b = 12
c = 32

You should have \(x=\dfrac{-b}{2a}\) ---> \(x=\dfrac{-(12)}{2(1)}\)

Does that make sense?

Answer 4

−6

Answer 5

Right

Now substitute -6 in for x in the original equation you had \(y=x^2+12x+32\)

Answer 6

y=-6^2+12x+32

Answer 7

Don't forget the second x

\(y=(-6)^2+12(-6)+32\)

Answer 8

so that's all i would put in

Answer 9

Solve for y

Answer 10

y=-4

Answer 11

Yeah

x = -6
y = -4

Points are written as \((x,y)\), so your vertex point is \((-6,-4)\)

Answer 12

thank you