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Algebra1B CPcreate a function that represents the path traveled by the kickball

Algebra1B CPcreate A Function That Represents The Path Traveled By The Kickball class=

Sagot :

Given that the ball travels 10 ft horizontally, then the maximum is reached at half of this distance, that is 5 ft. This means that the parabola has a maximum at (5, 25).

The equation of a parabola in vertex form is:

[tex]y=a(x-h)^2+k[/tex]

where (h, k) is the vertex.

Substituting with the vertex (5, 25) and the point (0,0) we get:

[tex]\begin{gathered} 0=a(0-5)^2+25 \\ 0=a\cdot25+25 \\ -25=a\cdot25 \\ -\frac{25}{25}=a \\ -1=a \end{gathered}[/tex]

And the function that models the path traveled by the ball is:

[tex]y=-(x-5)^2+25[/tex]

where y is the vertical distance, or height, in ft, and x is the horizontal distance, also in ft.

View image AndreaD782509
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