Question

What is the quadratic function that is created with roots at 2 and 4 and a vertex at (3, 1)? please show work

Answer 1

ok thr roots are given so
the quardratic equation can be written as--
\[y=a(x-2)(x-4)\\y=a(x^2-4x-2x+8)=a(x^2-6x+8)\]
ok?

Answer 2

now u have to find the value of the constant a,right?

Answer 3

ok..

Answer 4

now vertex=(3,1)
put x=3 and y=1 in the above equation and u'll find the value of a

Answer 5

so u'll get
\[1=a(3^2-6*3+8)\\a=-1\]
so the quadratic eq is--
\[y=-(x^2-6x+8)\]

Answer 6

ok?

Answer 7

y=−(x2−6x+8) is my final answer?

Answer 8

yup

Answer 9

ok thank u

Answer 10

yw!!