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Determine the type of function for the given expression:
[tex]\[ b(x) = 2x^2 + 5 \][/tex]

A. Quadratic
B. Linear
C. Exponential

Sagot :

GinnyAnsweridn
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
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