SOLUTION: A quadratic function has zeros at x=2 and x=4 and a y-intercept at -16. What is the quadratic function in standard form? I know I have to unfoil it, but I don't see how it is po

Question 513375: A quadratic function has zeros at x=2 and x=4 and a y-intercept at -16. What is the quadratic function in standard form?
I know I have to unfoil it, but I don't see how it is possible. If y=-16, wouldn't one of zeros have to be negative?
Found 2 solutions by oberobic, josmiceli:
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Unfoil tells us the equation is:
.
(x-4)(x-2) = 0
.
Foil tells us the equation is:
.
x^2 -2x -4x +8 = 0
x^2 -6x + 8 = 0
.
So, when x=0, y = 8.
.
In contrast, a y-intercept at -16 tells us the point is (0,-16).
.
Let's look at the graph of x^2-6*x+8.
.

.
Hmmm...
So, perhaps the graph is going the other way?
And to have a y-intercept of (0,-16), we perhaps need to multiply by the constant -2?
.
-2(x-4)(x-2) = 0

.
That seems to do it.
.
Done.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The general form is

The zeros:

and

-------------------
When ,

-----------
Now I have

(1)
and

(2)
Subtract (1) from (2)
(2)
(1)

and
(2)
(2)
(2)
The equation is:

check:
(2,0)

(4,0)

OK

RELATED QUESTIONS
Find a formula for the quadratic function whose graph has y-intercept at y=15 and zeros... (answered by ikleyn)
y=-2(x-(3+i))(x-(3-i)) a. What are the zeros of the quadratic function? b. Write the... (answered by josgarithmetic,ikleyn)
Find a formula for the quadratic function whose graph has y-intercept at y=15 and zeros... (answered by josgarithmetic)
What is a quadratic function in standard Form having zeros of -2 and... (answered by Boreal,josgarithmetic)
Find the rule of a quadratic function (in general form) whose graph has x intercepts at... (answered by josgarithmetic)
Find a formula for the quadratic function whose graph has y-intercept at y=13 and zeros... (answered by Boreal)
What is the function of a quadratic function with zeros at -5/2 and... (answered by Alan3354)
A quadratic function has zeros −3 and 5 and contains the point (4, 14). Find the... (answered by ewatrrr,ikleyn)
1) Write the quadratic function rule that has a vertex at (-2,5) and is stretched by a... (answered by greenestamps)