From the equation, find the axis of symmetry of the parabola. $y=2 x^2+4 x-1$
A. $x=3$
B. $x=-1$
C. $x=-3$
D. $x=1$

The axis of symmetry of the parabola y = 2 x 2 + 4 x − 1 is given by the equation x = − 1 . Therefore, the correct answer is option B. This line divides the parabola into two symmetrical halves.
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Answered by Anonymous | 2025-07-04

Identify the coefficients: a = 2 and b = 4 .
Apply the axis of symmetry formula: x = − 2 a b ​ .
Substitute the values: x = − 2 ( 2 ) 4 ​ .
Simplify to find the axis of symmetry: x = − 1 . The answer is x = − 1 ​ .

Explanation

Problem Analysis We are given the equation of a parabola y = 2 x 2 + 4 x − 1 . Our goal is to find the axis of symmetry.

Axis of Symmetry Formula The general form of a parabola is y = a x 2 + b x + c . The axis of symmetry for a parabola in this form is given by the formula x = − 2 a b ​ .

Identifying Coefficients In our equation, y = 2 x 2 + 4 x − 1 , we can identify the coefficients as a = 2 , b = 4 , and c = − 1 .

Calculating the Axis of Symmetry Now, we substitute the values of a and b into the axis of symmetry formula: x = − 2 ( 2 ) 4 ​ = − 4 4 ​ = − 1

Final Answer Therefore, the axis of symmetry of the parabola is x = − 1 .


Examples
Understanding the axis of symmetry is crucial in various real-world applications. For instance, when designing parabolic mirrors or satellite dishes, the axis of symmetry helps in focusing incoming signals or light to a single point. In architecture, knowing the axis of symmetry can aid in creating balanced and aesthetically pleasing parabolic arches. Furthermore, in physics, projectile motion follows a parabolic path, and the axis of symmetry helps determine the maximum height and range of the projectile.

Answered by GinnyAnswer | 2025-07-04