Question

Please help me!

For each set of conditions, write an appropriate quadratic function rule:

1. X-intercepts at (-4,0) and (12,0) and opening downward

2. X- intercepts at (-2,0) and (6,0) with y intercept at (0,-60)

3. X-intercepts at (-1,0) and (3,0) with a minimum at (1,-4)

Please help me!

Answer 1

for the first one you can start with
\[y=(x+4)(x-12)\] but since it opens down, you should make it
\[y=-(x+4)(x-12)\]

Answer 2

then i guess you have to multiply it out

Answer 3

thank you!!! do you have any idea on how to do the other two?

Answer 4

x intercepts at (-2,0) and (6,0) mean:
y = 0 when x=-2 and x=6, or:
(x - (-2))*(x-6) = 0, or (x+2)(x-6)=0

Answer 5

thnx :)

Answer 6

Now we just need the leading coefficient in front of those parentheses..
y = A(x+2)(x-6)
when x=0, y=-60:
-60 = A (-12), A=5.

Answer 7

So:
y = 5(x+2)(x-6) <-simplify.

Answer 8

ur first problem in a year