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ALGEBRA 1 QUESTION

Ingrid hit a golf ball. The height of the ball (in meters above the ground) t seconds after being hit is modeled by

h(t)=-5t^2+30t

1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation.

2) How many seconds after being hit does the ball reach its highest point?

__________seconds

Sagot :

thepingu

Answer:

[tex]\huge\boxed{\text{1. } h(t) = -5(t-3)^2 + 45}[/tex]

[tex]\huge\boxed{\text{2. 3 seconds}}[/tex]

Step-by-step explanation:

If we're looking for the point at with the ball reaches its highest point, we want to find the graph's vertex. In order to get the equation into a form with the vertex in it, we need to convert the equation into vertex form. This is an equation in the form [tex]y=a(x-h)^2 + k[/tex], h being the x value of the vertex, and k being the y value of the vertex.

In order to convert our equation, [tex]-5t^2+30t[/tex] into vertex form, we can algebraically manipulate it to get it into the form we want.

  • [tex]-5t^2 +30t[/tex]
  • [tex]-5 \cdot t^2 + 30t[/tex] (Separate the -5 from the t^2)
  • [tex]-5(t^2-6t+0)[/tex] (Factor out a -5)
  • [tex]-5(t^2 -6t + (-3)^2 - (-3)^2 + 0)[/tex] (Completing the Square)
  • [tex]-5((t-3)^2 - (-3)^2 + 0)[/tex] (Binomial Formula)
  • [tex]-5((t-3)^2 - 9)[/tex] (Simplify)
  • [tex]-5(t-3)^2 + 45[/tex] (Factor the -5 back in)

Therefore, our equation with the vertex in it is [tex]-5(t-3)^2 + 45[/tex]. To find the vertex, we can examine the equation to find the values of h and k in the formula  [tex]y=a(x-h)^2 + k[/tex] (where the vertex coordinates are (h, k)).

It seems that h is 3 and k is 45. Therefore, the coordinate of the vertex is (3, 45). Since it asks for how many seconds after being hit does the ball reach its highest point, we would take the x value since x represents seconds. This is 3. Therefore, the ball reaches its highest point after 3 seconds.

Hope this helped!

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