Question
8 Pr ectile Motion. A soccer ball is
kic ed from the ground. The height,
time
(i) Express the function in the form
kic ed from the ground. The height,
time
(i) Express the function in the form
Ask by Davey Klein. in Singapore
Jan 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Solution
To express the height function
-
Rearrange the Equation:
Begin by rewriting the equation in standard quadratic form: -
Factor Out the Common Term:
Factor out the coefficient of, which is : -
Factor the Quadratic Expression:
Now, factor the quadratic expression inside the parentheses: -
Combine the Factors:
Substitute the factored form back into the equation: -
Final Form:
This gives the function in the desired form:Simplifying further, it can be written as:
Final Answer:
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Simplify this solution Bonus Knowledge
To express the function
Next, we can factor out
Now, we can complete the square for the quadratic
Substituting back gives:
Thus, we have the function in vertex form but we need it in the product form. From
Now it’s clear in the desired form:
In this case,
