Question

Write the equation of the quadratic function with roots -1 and 1 and a vertex at (0,-3)

Answer 1

tmi

Answer 2

write in vertex form?

Answer 3

you have a choice of ways to do this, because you were given too much information
method one
you know it factors as \(a(x-1)(x+1)\) because you know the zeros
you just don't know \(a\)
but if you replace \(x\) by \(0\) and set the result equal to \(-3\) you will get it
\[a(0-1)(0+1)=-3\]
\[-a=-3\]\[a=3\]

Answer 4

method 2
you are given the vertex as \((0.-3)\) so you know it has to look like \(y=ax^2-3\)

Answer 5

this time find \(a\) since you are told if \(x=1\) then \(y=0\) solve
\[a-3=0\] and so \(a=3\) and it is \(3x^2-3\) again

Answer 6

okay now i need help with this one pleaseee Write the equation of the quadratic function with roots -10 and -8 and a vertex at (-9, -3).

Answer 7

same idea exactly

Answer 8

you want to use method one, or method two? makes no difference

Answer 9

method 2

Answer 10

vertex form is \(y=a(x-h)^2+k\) if the vertex is \((h,k)\)
in your case the vertex is \((-9,-3)\) so your first step would be to write
\[y=a(x+9)^2-3\]

Answer 11

your second step would be to replace \(x\) by \(-8\) and set the result equal to zero and solve for \(a\)
i.e. write
\[a(-8+9)^2-3=0\] or
\[a-3=0\] and now it should be easy

Answer 12

okay thanks :)