Identify The Axis Of Symmetry Of A Quadratic Functions From Equation Worksheet

Algebra 2
Quadratic Functions

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How Will This Worksheet on "Identify the Axis of Symmetry of a Quadratic Function from Equation" Benefit Your Student's Learning?

  • Helps students locate the highest or lowest point of the quadratic function, which is important for drawing and understanding the graph.
  • This is a crucial step in completing the square, a method used to solve quadratic equations.
  • Improves the ability to study how the quadratic function behaves, such as where it goes up or down.
  • Makes it easier to change quadratic functions into a different form (vertex form), helping with further calculations and transformations.

How to Identify the Axis of Symmetry of a Quadratic Functions from Equation?

  • First, ensure it is in the standard form \( ax^2 + bx + c \).
  • Note the values of \( a \) and \( b \) from the equation.
  • Use `x = -\frac{b}{2a}` to calculate the `x`-coordinate of the axis of symmetry.
  • The line `x = -\frac{b}{2a}` is the axis of symmetry for the quadratic function.

Solved Example

Q. Find the equation of the axis of symmetry for the parabola y=x2y = x^2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline\underline{\hspace{3cm}}
Solution:
  1. Identify Quadratic Equation: The general form of a quadratic equation is y=ax2+bx+cy = ax^2 + bx + c.\newline For the given parabola y=x2y = x^2, we can see that a=1a = 1, b=0b = 0, and cc is not relevant for finding the axis of symmetry.
  2. Use Axis of Symmetry Formula: The axis of symmetry for a parabola given by the equation y=ax2+bx+cy = ax^2 + bx + c is x=b2ax = -\frac{b}{2a}.\newline We will use this formula to find the axis of symmetry for the given parabola.
  3. Substitute Values: Substitute the values of aa and bb into the formula for the axis of symmetry: x=b2ax = -\frac{b}{2a}.\newline Here, a=1a = 1 and b=0b = 0, so x=021x = -\frac{0}{2\cdot 1}.
  4. Perform Calculation: Perform the calculation: x=021x = -\frac{0}{2\cdot 1} simplifies to x=0x = 0.\newlineSo, the axis of symmetry is at x=0x = 0.
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About Worksheet

Algebra 2
Quadratic Functions

To identify the axis of symmetry of a quadratic function from its equation \( ax^2 + bx + c \), use the formula `x = -\frac{b}{2a}`. This vertical line divides the graph into two mirror-image halves and passes through the vertex, ensuring that each point on one side of the axis has a corresponding point on the opposite side at an equal distance from the axis.

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