To determine the type of the given function [tex]\( b(x) = 2x^2 + 5 \)[/tex], we need to analyze its form and characteristics.
### Step-by-Step Solution:
1. Identify the Terms of the Function:
The given function is [tex]\( b(x) = 2x^2 + 5 \)[/tex].
2. Determine the Highest Power of [tex]\( x \)[/tex]:
- The term [tex]\( 2x^2 \)[/tex] includes [tex]\( x \)[/tex] raised to the power of 2.
- The term [tex]\( 5 \)[/tex] is a constant and does not change with [tex]\( x \)[/tex].
3. Categorize the Function Based on the Highest Degree:
- If the highest power of [tex]\( x \)[/tex] in the function is 2, the function is Quadratic.
- If the highest power of [tex]\( x \)[/tex] in the function is 1, the function is Linear.
- If the function has the form [tex]\( a \cdot b^x \)[/tex] (where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants and [tex]\( x \)[/tex] is an exponent), the function is Exponential.
4. Applying the Criteria:
- In [tex]\( b(x) = 2x^2 + 5 \)[/tex], the highest power of [tex]\( x \)[/tex] is [tex]\( 2 \)[/tex].
### Conclusion:
Since the highest power of [tex]\( x \)[/tex] in [tex]\( b(x) = 2x^2 + 5 \)[/tex] is 2, the function is Quadratic. Therefore, the answer is:
Quadratic
