Questions: Given that g(x)=2x^2-3x+4, find each of the following. a) g(0) b) g(-1) c) g(3) d) g(-x) e) g(1-t) b) g(-1)=9 (Simplify your answer.) c) g(3)=13 (Simplify your answer.) d) g(-x)=2x^2+3x+4 (Simplify your answer.) e) g(1-t)= (Simplify your answer.)

Given that g(x)=2x^2-3x+4, find each of the following. a) g(0) b) g(-1) c) g(3) d) g(-x) e) g(1-t) b) g(-1)=9 (Simplify your answer.) c) g(3)=13 (Simplify your answer.) d) g(-x)=2x^2+3x+4 (Simplify your answer.) e) g(1-t)= (Simplify your answer.)
Transcript text: Given that $g(x)=2 x^{2}-3 x+4$, find each of the following. a) $g(0)$ b) $g(-1)$ c) $g(3)$ d) $g(-x)$ e) $g(1-t)$ b) $g(-1)=9$ (Simplify your answer.) c) $g(3)=13$ (Simplify your answer.) d) $g(-x)=2 x^{2}+3 x+4$ (Simplify your answer.) e) $g(1-t)=$ $\square$ (Simplify your answer.)
failed

Solution

failed
failed

Solution Steps

Step 1: Calculate \( g(0) \)

To find \( g(0) \), substitute \( x = 0 \) into the function \( g(x) = 2x^2 - 3x + 4 \): \[ g(0) = 2(0)^2 - 3(0) + 4 = 0 - 0 + 4 = 4. \] Thus, \( g(0) = 4 \).

Step 2: Calculate \( g(-1) \)

To find \( g(-1) \), substitute \( x = -1 \) into the function \( g(x) = 2x^2 - 3x + 4 \): \[ g(-1) = 2(-1)^2 - 3(-1) + 4 = 2(1) + 3 + 4 = 2 + 3 + 4 = 9. \] Thus, \( g(-1) = 9 \).

Step 3: Calculate \( g(3) \)

To find \( g(3) \), substitute \( x = 3 \) into the function \( g(x) = 2x^2 - 3x + 4 \): \[ g(3) = 2(3)^2 - 3(3) + 4 = 2(9) - 9 + 4 = 18 - 9 + 4 = 13. \] Thus, \( g(3) = 13 \).

Final Answer

\[ \boxed{ \begin{aligned} a) \quad g(0) &= 4, \\ b) \quad g(-1) &= 9, \\ c) \quad g(3) &= 13. \end{aligned} } \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around at each zero. f(x)=4(x-1)(x-9)^2 Determine the zero(s). The zero(s) is/are (Type integers or decimals. Use a comma to separate answers as needed.) Determine the multiplicities of the zero(s). Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. A. There are two zeros. The multiplicity of the smallest zero is The multiplicity of the largest zero is (Simplify your answers.) B. There are three zeros. The multiplicity of the smallest zero is The multiplicity of the largest zero is The multiplicity of the other zero is . (Simplify your answers.) C. There is one zero. The multiplicity of the zero is (Simplify your answer.) Determine the behavior of the function at each zero. Select the correct choice below and, if necessary, fill in the answer boxes within your choice. A. The graph touches the x-axis and turns around at all zeros. B. The graph crosses the x-axis at all zeros.
failedAnswered
Factor the trinomial or state that the trinomial is prime. 3x^2-13x-10
failedAnswered
Question 6 HIV infection is diagnosed as AIDS when: a. a person tests positive for HIV antibodies b. the person develops a severe, life-threatening disease c. the T-cell count is less than 200 d. the B-cell count is less than 200 Moving to another question will save this response.
failedAnswered
Why is relative valuation considered more intuitive compared to absolute valuation?
failedAnswered
Which position would the nurse place the feet and legs in when caring for a client with peripheral arterial insufficiency? Place them slightly lower than the head and chest. Use pillows to support the heels above the mattress. Raise the knees using the knee gatch on the bed. Elevate feet by raising the foot of the bed on blocks.