Pre-cal with Algebra

Question

A ball is thrown upward and outward from a height of 6 feet. The height of the ball, 𝑓(𝑥), in feet, can be modeled by 𝑓(𝑥) = −0.6𝑥^2 + 2.7𝑥 + 6 where 𝑥 is the ball’s horizontal distance, in feet, from where it was thrown. Summarize your findings, using the following questions to guide your answers: What technique/strategy/formula did you use to find the maximum height and find the distance? Would the graph of this parabola open upward or downward? What is the vertex as an ordered pair? 

Answer 1

Hi Emma

If you are using Algebra on your given function the following strategies can be applied:

f(x) = -0.6x² + 2.7x + 6

Is a function in the form of f(x) = ax² + bx + c; the Standard/General for of a Quadratic Equation you can look up information associated with this form of the Quadratic Equation in your text or online.

When a is negative the parabola opens downward

The x coordinate, also called h of the vertex is -b/2a

The y coordinate, also called k of the vertex can be found by plugging whatever you get for -b/2a back into your function

You should compare the vertex coordinates to the value of a. If a is negative and your vertex is positive then your vertex is a maximum and will contain the maximum height

You can use the Quadratic Formula to find the distance in x traveled after the ball is thrown upward and outward from a height of 6 feet.

After you do the calculations to see your vertex a simple graph will confirm whether the vertex is a maximum or minimum. The distance traveled after the ball is thrown upward and outward from a height of 6 feet can also be seen. Remember distance is positive.

You can graph your function at Desmos.com

I hope this helps