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Question 5 (1 point)

Given the function below, state the equation of the axis of symmetry.

[tex]\[ y = 5x^2 + 20x + 1 \][/tex]

A. [tex]\( y = 19 \)[/tex]
B. [tex]\( x = -19 \)[/tex]
C. [tex]\( x = 2 \)[/tex]
D. [tex]\( x = -2 \)[/tex]

Sagot :

GinnyAnswer
To find the equation of the axis of symmetry for the given quadratic function [tex]\( y = 5x^2 + 20x + 1 \)[/tex], we can follow these steps:

1. Identify the coefficients: Look at the standard form of a quadratic equation, which is [tex]\( y = ax^2 + bx + c \)[/tex]. Here, the coefficients are:
- [tex]\( a = 5 \)[/tex]
- [tex]\( b = 20 \)[/tex]
- [tex]\( c = 1 \)[/tex] (although [tex]\( c \)[/tex] is not needed to find the axis of symmetry)

2. Use the formula for the axis of symmetry: The formula to find the axis of symmetry for a quadratic equation [tex]\( y = ax^2 + bx + c \)[/tex] is:
[tex]\[ x = -\frac{b}{2a} \][/tex]

3. Substitute the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] into the formula:
[tex]\[ x = -\frac{20}{2(5)} \][/tex]

4. Simplify the expression:
[tex]\[ x = -\frac{20}{10} = -2 \][/tex]

Hence, the equation of the axis of symmetry for the quadratic function [tex]\( y = 5x^2 + 20x + 1 \)[/tex] is [tex]\( x = -2 \)[/tex].

Therefore, the correct answer is:
[tex]\[ x = -2 \][/tex]
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