The car is speeding at a rate of 33.3mph
<h3>Speed and distance of an object</h3>
If a certain car going 60 mph can stop in 180 ft, then we can express this as:
To determine the speed for a car traveling at 100ft, we will have:
Take the ratio of the expression
60/x = 180/100
180x = 6000
x = 33.3mph
Hence the car is speeding at a rate of 33.3mph
learn more on speed here: brainly.com/question/4931057
When you have an equation f(x)=ax^2 + bx + c the vertex is (-b/2a,f(-b/2a))
so just plug into the formula, (-12/-2,f(-12/-2)) and (6,32) is the vertex.
Answer:
In the table, we can see values of x and y, to complete it, we just need to input the different values of x in the equation:
y = 16*x^2
For example in the first slot, we have x = -4
Then we will have:
y = 16*(-4)^2 = 240
Then we complete the empty slot with 240.
The table would be:
![\left[\begin{array}{cccccccccccccccc}x&-4&-3&-2.5&-2&-1.5&-1&-0.5&0&0.5&1&1.5&2&2.5&3&4\\y&240&\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccccccccccccccc%7Dx%26-4%26-3%26-2.5%26-2%26-1.5%26-1%26-0.5%260%260.5%261%261.5%262%262.5%263%264%5C%5Cy%26240%26%5Cend%7Barray%7D%5Cright%5D)
Now we just need to do the same for the other values:
y(-3) = 16*(-3)^2 = 144
y(-2.5) = 16*(-2.5)^2 = 100
y(-2) = 16*(-2)^2 = 64
y(-1.5) = 16*(-1.5)^2 = 36
y(-1) = 16*(-1)^2 = 16
y(-0.5) = 16*(-0.5)^2 = 4
y(0) = 16*(0)^2 = 0
y(0.5) = 16*(0.5)^2 = 4
y(1) = 16*(1)^2 = 16
y(1.5) = 16*(1.5)^2 = 36
y(2) = 16*(2)^2 = 64
y(2.5) = 16*(2.5)^2 = 100
y(3) = 16*(3)^2 = 144
y(4) = 16*(4)^2 = 240
Then the complete table is:
![\left[\begin{array}{cccccccccccccccc}x&-4&-3&-2.5&-2&-1.5&-1&-0.5&0&0.5&1&1.5&2&2.5&3&4\\y&240&144&100&64&36&16&4&0&4&16&36&64&10&144&240\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccccccccccccccc%7Dx%26-4%26-3%26-2.5%26-2%26-1.5%26-1%26-0.5%260%260.5%261%261.5%262%262.5%263%264%5C%5Cy%26240%26144%26100%2664%2636%2616%264%260%264%2616%2636%2664%2610%26144%26240%5Cend%7Barray%7D%5Cright%5D)
Then we can see that there is a symmetry around the value x = 0.