Question

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find the following for the function \\(f(x) = 4x^2 + 2x - 2\\).

(a) \\(f(0)\\)
(b) \\(f(5)\\)
(c) \\(f(-5)\\)
(d) \\(f(-x)\\)
(e) \\(-f(x)\\)
(f) \\(f(x + 3)\\)
(g) \\(f(3x)\\)
(h) \\(f(x + h)\\)

part 1 of 8

(a) \\(f(0) =\\) (simplify your answer.)

Explanation:

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<reasoning>

Identify the given function

We are given the quadratic function:
\[f(x) = 4x^2 + 2x - 2\]

Evaluate the function at zero

Using the Definition of a Function knowledge point:
\[

$$\begin{aligned} f(0) &= 4(0)^2 + 2(0) - 2 \\ f(0) &= 0 + 0 - 2 \\ f(0) &= -2 \end{aligned}$$

\]
</reasoning>

<answer>
For the function \(f(x) = 4x^2 + 2x - 2\), find the following:

(a) \(f(0) =\) <blank>-2</blank>
</answer>

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Answer:

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Identify the given function

We are given the quadratic function:
\[f(x) = 4x^2 + 2x - 2\]

Evaluate the function at zero

Using the Definition of a Function knowledge point:
\[

$$\begin{aligned} f(0) &= 4(0)^2 + 2(0) - 2 \\ f(0) &= 0 + 0 - 2 \\ f(0) &= -2 \end{aligned}$$

\]
</reasoning>

<answer>
For the function \(f(x) = 4x^2 + 2x - 2\), find the following:

(a) \(f(0) =\) <blank>-2</blank>
</answer>

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