Question
6. [-/1 Points] DETAILS MY NOTES TGEIALG6 5.4.016. Complete the solution. Evaluate \( -2 x^{2}+7 x-1 \) for \( x=-2 \) \[ \begin{array}{l}-2 x^{2}+7 x-1=-2(\square)^{2}+7(\square)-1 \\ =-2(\square)+7(\square)-1 \\ =\square+(-14)-1 \\ =\square \\ \text { SUBMIT ANSWER }\end{array} \]
Ask by Morrison Park. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Evaluate \( -2x^{2} + 7x - 1 \) for \( x = -2 \):
\[
-2(-2)^{2} + 7(-2) - 1 = -8 - 14 - 1 = -23
\]
So, the answer is \(-23\).
Solution
To evaluate the expression \( -2x^{2} + 7x - 1 \) for \( x = -2 \), we will substitute \( -2 \) into the expression step by step.
1. **Substituting \( x = -2 \)**:
\[
-2(-2)^{2} + 7(-2) - 1
\]
2. **Calculating \( (-2)^{2} \)**:
\[
(-2)^{2} = 4
\]
3. **Substituting back into the expression**:
\[
-2(4) + 7(-2) - 1
\]
4. **Calculating \( -2(4) \)**:
\[
-2(4) = -8
\]
5. **Calculating \( 7(-2) \)**:
\[
7(-2) = -14
\]
6. **Putting it all together**:
\[
-8 - 14 - 1
\]
7. **Calculating the final result**:
\[
-8 - 14 = -22
\]
\[
-22 - 1 = -23
\]
Thus, the final answer is:
\[
\boxed{-23}
\]
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Mind Expander
To evaluate the expression \( -2 x^{2} + 7 x - 1 \) for \( x = -2 \), we start by plugging in \(-2\) for \(x\). First, calculate \( -2 (-2)^{2} + 7(-2) - 1 \): 1. Calculate \( (-2)^{2} = 4 \). 2. Plug it into the equation: \( -2(4) + 7(-2) - 1 = -8 - 14 - 1 \). 3. Combine the values: \( -8 - 14 = -22 \), and then \( -22 - 1 = -23 \). Thus, the final result is \( -23 \). Now, the steps can be expressed in the equation format: \[ -2 (-2)^{2} + 7(-2) - 1 = -8 + (-14) - 1 = -23 \] So the completed solution is \( -23 \).
