Question

a baseball player throws a ball upward from 2 feet above the ground. the height of the ball, \\(h(t)\\), in feet, at time \\(t\\), in seconds, is modeled by a quadratic function represented in the table.

\\(\

$$\begin{array}{|c|c|c|c|}\\hline t & 0 & 1 & 2 \\\\ \\hline h(t) & 2 & 14 & 2 \\\\ \\hline\\end{array}$$

\\)

write a quadratic function in vertex form to represent \\(h(t)\\).

\\(h(t) = 12(t - 1)^2 - 14\\)
\\(h(t) = -12(t - 1)^2 - 14\\)
\\(h(t) = 12(t - 1)^2 + 14\\)
\\(h(t) = -12(t - 1)^2 + 14\\)

Explanation:

Identify the vertex from the table

Using the Vertex Form of a Quadratic knowledge point

$$
LATEXBLOCK0
$$

Set up the vertex form equation

Using the Vertex Form of a Quadratic knowledge point

$$
LATEXBLOCK1
$$

Solve for the leading coefficient

Using the Quadratic Functions knowledge point

$$
LATEXBLOCK2
$$

Write the final quadratic function

Using the Vertex Form of a Quadratic knowledge point

$$ h(t) = -12(t - 1)^2 + 14 $$

Answer:

• (A) \(h(t) = 12(t-1)^2 - 14\)
• (B) \(h(t) = -12(t-1)^2 - 14\)
• (C) \(h(t) = 12(t-1)^2 + 14\)
• (D) \(h(t) = -12(t-1)^2 + 14\) (Correct answer)