Answer :
To find \( p(|-3|) \) for the given function \( p(m) = 2m^2 - 4m + 3 \), we will follow these steps:
1. Determine the absolute value: First, we need to find the value of \(|-3|\).
- The absolute value of \(-3\) is \( 3 \).
So, \(|-3| = 3\).
2. Substitute into the function: Next, substitute \( m = 3 \) into the function \( p(m) \).
- The function is given by \( p(m) = 2m^2 - 4m + 3 \).
Therefore, we need to evaluate \( p(3) \).
3. Calculate \( p(3) \):
- Substitute \( m = 3 \) into the function:
[tex]\[ p(3) = 2(3)^2 - 4(3) + 3 \][/tex]
4. Simplify the expression:
- First, calculate \( (3)^2 \):
[tex]\[ (3)^2 = 9 \][/tex]
- Next, multiply by 2:
[tex]\[ 2 \times 9 = 18 \][/tex]
- Calculate \( 4 \times 3 \):
[tex]\[ 4 \times 3 = 12 \][/tex]
- Now, plug these values back into the expression:
[tex]\[ p(3) = 18 - 12 + 3 \][/tex]
- Combine the terms:
[tex]\[ 18 - 12 = 6 \][/tex]
[tex]\[ 6 + 3 = 9 \][/tex]
Thus, the value of \( p(|-3|) \) is \( 9 \).
Therefore, the correct answer is [tex]\( \boxed{9} \)[/tex].
1. Determine the absolute value: First, we need to find the value of \(|-3|\).
- The absolute value of \(-3\) is \( 3 \).
So, \(|-3| = 3\).
2. Substitute into the function: Next, substitute \( m = 3 \) into the function \( p(m) \).
- The function is given by \( p(m) = 2m^2 - 4m + 3 \).
Therefore, we need to evaluate \( p(3) \).
3. Calculate \( p(3) \):
- Substitute \( m = 3 \) into the function:
[tex]\[ p(3) = 2(3)^2 - 4(3) + 3 \][/tex]
4. Simplify the expression:
- First, calculate \( (3)^2 \):
[tex]\[ (3)^2 = 9 \][/tex]
- Next, multiply by 2:
[tex]\[ 2 \times 9 = 18 \][/tex]
- Calculate \( 4 \times 3 \):
[tex]\[ 4 \times 3 = 12 \][/tex]
- Now, plug these values back into the expression:
[tex]\[ p(3) = 18 - 12 + 3 \][/tex]
- Combine the terms:
[tex]\[ 18 - 12 = 6 \][/tex]
[tex]\[ 6 + 3 = 9 \][/tex]
Thus, the value of \( p(|-3|) \) is \( 9 \).
Therefore, the correct answer is [tex]\( \boxed{9} \)[/tex].
