# A Toy Rocket Was Launched From The Ground The Function F X 16×2 192x Algebra Help

need help with these

1. A toy rocket was launched from the ground. The function f(x) = -16×2 + 192x shows the height of the rocket f(x), in feet, from the ground at time x seconds.

What is the axis of symmetry of the graph of f(x), and what does it represent? (3 points)

x = 12; it takes 12 seconds to reach the maximum height and 12 seconds to fall back to the groundx = 12; it takes 12 seconds to reach the maximum height and 24 seconds to fall back to the groundx = 6; it takes 6 seconds to reach the maximum height and 6 seconds to fall back to the groundx = 6; it takes 6 seconds to reach the maximum height and 3 seconds to fall back to the ground

3. Water coming out from a fountain is modeled by the function f(x) = -x2 + 7x + 5 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds.

What does the average rate of change of f(x) from x = 4 to x = 6 represent? (4 points)

The water falls down with an average speed of 5 feet per second from 4 seconds to 6 seconds.The water falls down with an average speed of 3 feet per second from 4 seconds to 6 seconds.The water travels an average distance of 5 feet from 4 seconds to 6 seconds.The water travels an average distance of 3 feet from 4 seconds to 6 seconds.

4. Functions f(x) and g(x) are shown below:

f(x) = x2
g(x) = x2 – 20x + 100

In which direction and by how many units should f(x) be shifted to obtain g(x)? (4 points)

Right by 5 unitsLeft by 5 unitsRight by 10 unitsLeft by 10 units

5. Which of the following tables shows the correct steps to transform x2 + 10x + 24 = 0 into the form (x – p)2 = q?

[p and q are integers] (4 points)

Step 1×2 + 10x + 24 – 1 = 0 – 1Step 2×2 + 10x + 23 = -1Step 3(x + 5)2 = -1Step 1×2 + 10x + 24 – 2 = 0 – 2Step 2×2 + 10x + 22 = -2Step 3((x + 5)2 = -2Step 1×2 + 10x + 24 + 2 = 0 + 2Step 2×2 + 10x + 26 = 2Step 3((x + 5)2 = 2Step 1×2 + 10x + 24 + 1 = 0 + 1Step 2×2 + 10x + 25 = 1Step 3(x + 5)2 = 1

6. Solve 2×2 + 3x + 6 = 0. Round solutions to the nearest hundredth. (4 points)x ≈ -2.64 and x ≈ 1.14x ≈ -1.14 and x ≈ 2.64No real solutionsx ≈ -1.11 and x ≈ -4.89

9. David kicks a soccer ball off the ground and in the air, with an initial velocity of 35 feet per second. Using the formula H(t) = -16t2 + vt + s, what is the maximum height the soccer ball reaches? (4 points)17.9 feet18.2 feet18.7 feet19.1 feet

Type: MC

13. The table below shows the values of f(x) and g(x) for different values of x. One of the functions is a quadratic function, and the other is an exponential function. Which function is most likely increasing exponentially? (4 points)

xf(x)g(x)1332693112741881527243f(x), because it eventually exceeds g(x)g(x), because it eventually exceeds f(x)f(x), because it eventually intersects g(x)g(x), because it will not intersect f(x)