Question

what about this one @ivettef365

Answer 1

the equation of a parabola is written in the form: \({y=a(x-h)^2+k}\) where \((h,k)\) is the vertex

Answer 2

you know that \((h,k)\), the vertex, is \((3,-3)\)
and we know that a point, \((x,y)\), exist as \((0,-2)\)

using this we can plug in this information into the equation to find the value of \(a\):\[-2=a(0-3)^2+(-3)\]

Answer 3

Now if you solve that for a:\[-2=a(0-3)^2-3\]\[-2=a(-3)^2-3\]\[-2=a(9)-3\]\[-2=9a-3\]\[~~~1=9a\]\[~~{1\over9}=a\]
\[\large a={1\over9}\]

Answer 4

now we have all the pieces of information needed to write the equation
\[\large{y={1\over9}(x-3)^2-3}\]

Answer 5

ooooi thought you just had to plug in everything but thank you so much

Answer 6

we did plug in everything :)
except when writing an equation you have to leave out the \(x\) and \(y\) or else its not an equation anymore...the equation has to work for every \(x\) and \(y\) point on the parabola

Answer 7

is it the same for this

Answer 8

yup, you do exactly what we did for the previous one! :)

Answer 9

because i got y=(x+2)^2-1?

Answer 10

\[1=a(-1+2)^2-1\]\[1=a-1\]\[a=2\]so:\[y=2(x+2)^2-1\] you forgot the 2 :)

Answer 11

ooooo ok