Question

determine whether the statement is true or false. if the statement is false, make the necessary change(s) to produce a true statement.

the vertex of the parabola described by (f(x) = 4(x - 4)^2 - 2) is at ((4,2)).

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the statement is false. one way to correct the statement is, the function (f(x) = 4(x - 4)^2 - 2) does not describe a parabola.
b. the statement is false. one way to correct the statement is, the vertex of the parabola described by (f(x) = 4(x - 4)^2 - 2) is at (type an ordered pair.)
c. the statement is true.

Explanation:

Identify the given function and statement

The given statement is: "The vertex of the parabola described by \(f(x) = 4(x - 4)^2 - 2\) is at \((4, 2)\)."

Analyze the vertex form of the quadratic function

Using the Vertex Form of a Quadratic knowledge point

$$
LATEXBLOCK0
$$

Determine the vertex of the given function

Using the Vertex Form of a Quadratic knowledge point

$$
LATEXBLOCK1
$$

Evaluate the statement and select the correction

The original statement claims the vertex is at \((4, 2)\), which is false because the correct vertex is \((4, -2)\).
Therefore, the statement is false, and the correct option is B, with the ordered pair \((4, -2)\).

Answer:

• (A) The statement is false. One way to correct the statement is, the function \(f(x) = 4(x - 4)^2 - 2\) does not describe a parabola.
• (B) The statement is false. One way to correct the statement is, the vertex of the parabola described by \(f(x) = 4(x - 4)^2 - 2\) is at \((4, -2)\). (Correct answer)
• (C) The statement is true.