QUESTION 1
The given function is
![y = - 6x - 13](https://tex.z-dn.net/?f=y%20%3D%20-%206x%20-%2013)
The domain of this function refers to all values of x for which y is defined.
The given function is defined for all real values of x.
The domain is all real numbers.
The correct answer is A
QUESTION 2
The equation in column 1 is
![y = - 2 {x}^{2} - 4x + 12](https://tex.z-dn.net/?f=y%20%3D%20-%202%20%7Bx%7D%5E%7B2%7D%20-%204x%20%2B%2012)
We obtain the vertex form as follows;
![y = - 2( {x}^{2} + 2x) + 12](https://tex.z-dn.net/?f=y%20%3D%20-%202%28%20%7Bx%7D%5E%7B2%7D%20%2B%202x%29%20%2B%2012)
![y = - 2( {x}^{2} + 2x + {1}^{2}) - - 2 {(1)}^{2} + 12](https://tex.z-dn.net/?f=y%20%3D%20-%202%28%20%7Bx%7D%5E%7B2%7D%20%2B%202x%20%2B%20%7B1%7D%5E%7B2%7D%29%20-%20-%202%20%7B%281%29%7D%5E%7B2%7D%20%2B%2012)
![y = - 2({(x + 1)}^{2}) + 2 + 12](https://tex.z-dn.net/?f=y%20%3D%20-%202%28%7B%28x%20%2B%201%29%7D%5E%7B2%7D%29%20%2B%202%20%2B%2012)
![y = - 2({x + 1)}^{2} + 14](https://tex.z-dn.net/?f=y%20%3D%20-%202%28%7Bx%20%2B%201%29%7D%5E%7B2%7D%20%2B%2014)
The x-value of the vertex is -1.
The equation in column 2 is
![y = {x}^{2} - 4x + 3](https://tex.z-dn.net/?f=y%20%3D%20%7Bx%7D%5E%7B2%7D%20-%204x%20%2B%203)
We can also find the x-value of the vertex using the formula,
![x = - \frac{b}{2a}](https://tex.z-dn.net/?f=x%20%3D%20-%20%5Cfrac%7Bb%7D%7B2a%7D%20)
![x = - \frac{ - 4}{2(1)}](https://tex.z-dn.net/?f=x%20%3D%20-%20%5Cfrac%7B%20-%204%7D%7B2%281%29%7D%20)
![x = 2](https://tex.z-dn.net/?f=x%20%3D%202)
The correct answer is
B) The value found in column #1 is less than the value found in column #2
QUESTION 3
The height of the ball is modeled by
![h(t) = - 16 {t}^{2} + 64t](https://tex.z-dn.net/?f=h%28t%29%20%3D%20-%2016%20%7Bt%7D%5E%7B2%7D%20%2B%2064t)
where t equals the time in seconds and h(t) represents the height of the ball at time t seconds.
The axis of symmetry can be found using the formula,
![t = - \frac{b}{2a}](https://tex.z-dn.net/?f=t%20%3D%20-%20%5Cfrac%7Bb%7D%7B2a%7D%20)
![t = - \frac{ 64}{2( - 16)}](https://tex.z-dn.net/?f=t%20%3D%20-%20%5Cfrac%7B%2064%7D%7B2%28%20-%2016%29%7D%20)
![t = 2](https://tex.z-dn.net/?f=t%20%3D%202)
The correct answer is
A) t=2; it takes 2 seconds to reach maximum height and 2 seconds to fall back to the ground
QUESTION 4
The equation of axis of symmetry is given by the formula,
![x = - \frac{b}{2a}](https://tex.z-dn.net/?f=x%20%3D%20-%20%5Cfrac%7Bb%7D%7B2a%7D%20)
For the axis of symmetry of a given quadratic function to be zero, then the b-value of quadratic function should be zero.
The only equation from the given options whose b-value is zero is
![y = {x}^{2} + 2](https://tex.z-dn.net/?f=y%20%3D%20%7Bx%7D%5E%7B2%7D%20%2B%202)
The axis of symmetry is
![x = - \frac{0}{2(1)}](https://tex.z-dn.net/?f=x%20%3D%20-%20%5Cfrac%7B0%7D%7B2%281%29%7D%20)
![x = 0](https://tex.z-dn.net/?f=x%20%3D%200)
The correct answer is C