Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

PLZ DON'T TROLL ACTUALLY ANSWER THE QUESTION CORRECTLY
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!

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.