What is the axis of symmetry of quadratic function f(x)=-2x^2-(1/2)

In summary, the axis of symmetry is a line that divides a shape or graph into two equal halves, such as a parabola in a quadratic function. To find the axis of symmetry, you can use the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. The axis of symmetry represents the line of symmetry in the parabola and can only have one in a quadratic function. The value of a affects the direction and width of the parabola, with a positive value resulting in an upward opening parabola and a negative value resulting in a downward opening parabola.
  • #1
Lucas7105
1
0
The problem is:
f(x)=-2x^2-(1/2)
Determine if this statement is true of false:
The axis of symmetry is x=-2.
What is the axis of symmetry? How can you figure out the axis of symmetry without a b value, since the formula for it is x=-b/2a
 
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  • #2
Hello, and welcome to MHB! (Wave)

What if you write the given function in the equivalent form:

\(\displaystyle f(x)=-2x^2+0x-\frac{1}{2}\)
 
  • #3
Can someone tell me how to even remember all this? I watch at this and don't understand.
 

FAQ: What is the axis of symmetry of quadratic function f(x)=-2x^2-(1/2)

1. What is an axis of symmetry?

The axis of symmetry is a line that divides a shape or graph into two equal halves. In the case of a quadratic function, it is a vertical line that passes through the vertex of the parabola.

2. How do you find the axis of symmetry of a quadratic function?

To find the axis of symmetry of a quadratic function, you can use the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in the form of ax^2 + bx + c.

3. What does the axis of symmetry represent in a quadratic function?

The axis of symmetry represents the line of symmetry in the parabola. It is the point where the parabola changes direction from increasing to decreasing or vice versa.

4. Can a quadratic function have more than one axis of symmetry?

No, a quadratic function can only have one axis of symmetry. This is because the axis of symmetry is determined by the values of a and b in the quadratic equation, and these values cannot change.

5. How does the value of a affect the axis of symmetry in a quadratic function?

The value of a in a quadratic function determines the direction and width of the parabola. A positive value of a will result in a parabola opening upwards, and the axis of symmetry will be a minimum point on the graph. A negative value of a will result in a parabola opening downwards, and the axis of symmetry will be a maximum point on the graph.

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