2 1/4 as an improper fraction is 9/4
7/4 means you have to do 7 divided 4. You would get 1.75 then you have to do 1.75 times -4. You get -7. -7 is the answer.
Answer:
y = 1/12 (x − 5)²
Step-by-step explanation:
We can solve this graphically without doing calculations.
The y component of the focus is y = 3. Since this is above the directrix, we know this is an upward facing parabola, so it must have a positive coefficient. That narrows the possible answers to A and C.
The x component of the focus is x = 5. Since this is above the vertex, we know the x component of the vertex is also x = 5.
So the answer is A. y = 1/12 (x−5)².
But let's say this wasn't a multiple choice question and we needed to do calculations. The equation of a parabola is:
y = 1/(4p) (x − h)² + k
where (h, k) is the vertex and p is the distance from the vertex to the focus.
The vertex is halfway between the focus and the directrix. So p is half the difference of the y components:
p = (3 − (-3)) / 2
p = 3
k, the y component of the vertex, is the average:
k = (3 + (-3)) / 2
k = 0
And h, the x component of the vertex, is the same as the focus:
h = 5
So:
y = 1/(4×3) (x − 5)² + 0
y = 1/12 (x − 5)²
Answer:
Where are the graphs
Step-by-step explanation:
Answer:
roots: 1 and 3
k = 3
Step-by-step explanation:
2 roots: p and p+2
(x-p) (x-p-2) = x² - 4x + k
x² -2px -2x + p² + 2p = x² - 2 (p+1)x + (p² + 2p) = x² -4x + k
-2 (p+1) = -4
p+1 = 2
p = 1 ... root 1
p' = 1+2 = 3 ... root 2
k = p² + 2p = 3
check: (x-1) (x-3) = x² - 4x + 3 = x² - 4x + k
