Answer:
h(t) = -5*t^2 + 20*t + 2
Step-by-step explanation:
First, we know that the motion equation of the ball will be quadratic, so we write the equation:
h(t) = a*t^2 + b*t + c
Now we need to work with the data in the table.
h(1) = 17
h(3) = 17
h(1) = h(2) = 17
Then we have a symmetry around:
(3 - 1)/2 + 1 = 2
Remember that the symmetry is around the vertex of the parabola, then we can conclude that the vertex of the parabola is the point:
(2, h(2)) = (2, 22)
Remember that for a quadratic equation:
y = a*x^2 + b*x + c
with a vertex (h, k)
we can rewrite our function as:
y = a*(x - h)^2 + k
So in this case, we can rewrite our function as:
h(t) = a*(t - 2)^2 + 22
To find the value of a, notice the first point in the table:
(0, 2)
then we have:
h(0) = 2 = a*(0 - 2)^2 + 22
= 2 = a*(-2)^2 + 22
2 = a*(4) + 22
2 - 22 = a*(4)
-20/4 = -5 = a
Then our function is:
h(t) = -5*(t - 2)^2 + 22
Now we just expand it:
h(t) = -5*(t^2 - 4*t + 4) + 22
h(t) = -5*t^2 + 20*t + 2
The correct option is the first one.
What subject is this? ill comment the answer when i know
Answer: This is equivalent to 100% correct
Don’t know what you did there but is the scoreStep-by-step explanation:
Answer:
m+n=9
Step-by-step explanation:
Put the equation into the form ka^mb^n by multiplying the coefficients (-1*2*-3), so k= 6, then add the exponents of a together, a^2+a^1= a^3, m=3.
Now you have 6a^3, next we do the exponents of b together, b^3, b^2, b^1= b^6, n=6.
This is 6a^3b^6. m=3 and b=6, so add m+n=9.
