Answer:
3.3in
Step-by-step explanation:
Answer:
a=5
Step-by-step explanation:
Answer:
C - f(t) = 4(t − 1)^2 + 2; the minimum height of the roller coaster is 2 meters from the ground.
Step-by-step explanation:
Here we're asked to rewrite the given equation f(t) = 4t^2 − 8t + 6 in the form f(t) = a(t - h)^2 + k (which is known as the "vertex form of the equation of a parabola.") Here (h, k) is the vertex and a is a scale factor.
Let's begin by factoring 4 out of all three terms:
f(t) = 4 [ t^2 - 2t + 6/4 ]
Next, we must "complete the square" of t^2 - 2t + 6/4; in other words, we must re-write this expression in the form (t - h)^2 + k.
(To be continued)
Hello,
The rate of change is the slope (rise/run, y/x). To find that, we use the equation (y2-y1) over (x2-x1). It means take the second "y" and subtract it from the first "y" and the same to "x". If I plug in the numbers, it would be (3-6) over (5-4), and after you subtract, the answer simplifies to: -3/ 1 which is -3. Yay! We got the slope (rate of change) done.
Now let's find the y-intercept by using the formula of point-slope form,
y-y1= m (slope) (x-x1). This is saying you "y" is subtracted from the first
"y" of the points which equals the slope (m) times the quantity of "x" subtracted by the first "x" of the points.
Let's plug the numbers in: y-6 = -3 (x-4). Let's distribute -3 to the parenthesis, and after that it should simplify to: y-6 = -3x + 12. To get "y" by itself, add 6 to both sides: y = -3x +18. We have finally found the slope-intercept equation for those two points (4,6) and (5,3). To then find the y-intercept in this equation, it would be the 18, because -3 is the slope, so that makes 18 the y-intercept.
In conclusion, the rate of change is -3 and the y-intercept is 18.
I hope this helps!
May
You need to add what the lines are if you want them to be analysed for you^^
