Question

given the function $f(x)=7x^2 + 8x - 2$. calculate the following values: $f(0) = $ $f(2) = $ $f(-2) = $ $f(x + 1) = $ $f(-x) = $ question help: video

Explanation:

Step1: Calculate \( f(0) \)

Substitute \( x = 0 \) into \( f(x) = 7x^2 + 8x - 2 \).
\( f(0) = 7(0)^2 + 8(0) - 2 = 0 + 0 - 2 = -2 \)

Step2: Calculate \( f(2) \)

Substitute \( x = 2 \) into \( f(x) = 7x^2 + 8x - 2 \).
\( f(2) = 7(2)^2 + 8(2) - 2 = 7(4) + 16 - 2 = 28 + 16 - 2 = 42 \)

Step3: Calculate \( f(-2) \)

Substitute \( x = -2 \) into \( f(x) = 7x^2 + 8x - 2 \).
\( f(-2) = 7(-2)^2 + 8(-2) - 2 = 7(4) - 16 - 2 = 28 - 16 - 2 = 10 \)

Step4: Calculate \( f(x + 1) \)

Substitute \( x = x + 1 \) into \( f(x) = 7x^2 + 8x - 2 \).
\( f(x + 1) = 7(x + 1)^2 + 8(x + 1) - 2 \)
Expand \( (x + 1)^2 = x^2 + 2x + 1 \):
\( f(x + 1) = 7(x^2 + 2x + 1) + 8x + 8 - 2 = 7x^2 + 14x + 7 + 8x + 8 - 2 = 7x^2 + 22x + 13 \)

Step5: Calculate \( f(-x) \)

Substitute \( x = -x \) into \( f(x) = 7x^2 + 8x - 2 \).
\( f(-x) = 7(-x)^2 + 8(-x) - 2 = 7x^2 - 8x - 2 \)

Answer:

\( f(0) = -2 \)
\( f(2) = 42 \)
\( f(-2) = 10 \)
\( f(x + 1) = 7x^2 + 22x + 13 \)
\( f(-x) = 7x^2 - 8x - 2 \)