Homework Question

[HelpMehhhhh]

Write the equation for the family of quartic functions with a turning point at (2, 0) and x intercepts at x = 3
and x = −4. Then determine the member of that family that has a y intercept of −12.

new unit we started and the homework is due today, I tried to figure it out but I can't understand it as they don't give any other points and the 'member of that family' confuses me even further

 

[tkhunny]

"family" means only that you will not be completely specifying a single function. Just build in ALL the conditions offered..

Point: (2,0) - Notice how that is an x-intercept. (x-2) is a factor.)
Turning Point at (2,0) - That means (x-2)^2 is a factor
x-intercept at x = 3 - What does that mean?
x-intercept at x = -4 - What does that mean?
y-intercept at y = -12 - What does that mean?