can someone help me with this please

Question

You are playing baseball with a friend and accidently hit the ball over your neighbor’s house and into their backyard. The following questions are about the ball’s movement from when you hit the ball to when it hits the ground in your neighbor’s yard. 

a.   In a paint app or by printing the grid and then inserting a photo, draw a graph of what the ball’s movement could be. Height should be your dependent variable and distance should be your independent variable.  

b.   Describe the graph. What are the intercepts? What kind of function models this situation? What is the domain for the situation? What is the range for the situation? Is there a vertex or turning points? What are the coordinates for those points?

c.    Write the equation for your graph in vertex form and factored form. Label each form and explain what each part of the equation corresponds to in the graph.

Answer 1

Hello Zack! When I began recording this video the question had no answers; here is a video solution showing how to model the baseball's flight path with a quadratic equation, as well as how to obtain factored form, vertex form, and the important values like x-intercepts and the vertex coordinates. For this video I selected a basic quadratic equation to use as a demonstration; you are given the freedom in this problem to choose your own unique quadratic equation to model the baseball's flight path. For any projectile motion problems, remember to choose a quadratic equation with a negative x² term! Please reach out to me if you have any questions or would like further clarification! Best wishes :)

(Also a bit that I forgot to include in the video; also remember to label your y-intercept! My function has one at (0, 8) though I forgot to label or discuss it; instead I only show the x-intercepts and how to find them. You can find the y-intercept by substituting 0 for x in your quadratic equation. Also, the notation I used to represent the domain and range is interval notation, though I believe I mistakenly said "intercept notation".)

Answer 2

A ball in the air follows a parabolic path, so your graph should look something like an upside-down parabola, where the vertex would be in the first quadrant. If your units for height are in feet, you can say that there is a y-intercept at y=3, to represent how you hit the ball at some distance above the ground. There would be an x-intercept at some negative value near 0, and another at some relatively large distance from 0 (where you hit the ball from). The domain of the function that you are probably interested in in this case would be from 0 to wherever the ball lands, and your range would be from 0 to the y-coordinate of your vertex (which is the max height of the ball). You can probably use Desmos to generate a graph with these specifications.