How to find the axis of symmetry?
Understand the Problem
The question is asking how to identify the axis of symmetry for a given function or a geometric figure. The axis of symmetry is a line that divides the figure into two mirrored halves, and for a quadratic function, it can often be found using the formula x = -b / (2a) where the function is in the form ax^2 + bx + c.
Answer
$x = -\frac{b}{2a}$
Answer for screen readers
The axis of symmetry is found using the formula $x = -\frac{b}{2a}$.
Steps to Solve
- Identify the coefficients a and b
Locate the coefficients a and b in the quadratic equation $ax^2 + bx + c$.
- Use the axis of symmetry formula
The formula for the axis of symmetry of a parabola given by the quadratic function $ax^2 + bx + c$ is $x = -\frac{b}{2a}$. $$x = -\frac{b}{2a}$$
- Plug in the values of a and b
Substitute the values of a and b from the quadratic equation into the formula.
- Simplify the expression
Perform the division and simplification to find the x-value, which represents the axis of symmetry.
The axis of symmetry is found using the formula $x = -\frac{b}{2a}$.
More Information
The axis of symmetry helps to identify the vertex of the parabola and is crucial in graphing quadratic functions.
Tips
A common mistake is to mix up the signs when substituting the values of b and a. Be careful with negative signs and ensure accurate division.
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