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 ax2+bx+c.
  • Note the values of a and b from the equation.
  • Use x=-b2a to calculate the x-coordinate of the axis of symmetry.
  • The line x=-b2a is the axis of symmetry for the quadratic function.

Solved Example

Q. Find the equation of the axis of symmetry for the parabola y=x2. Simplify any numbers and write them as proper fractions, improper fractions, or integers.
Solution:
  1. Identify Quadratic Equation: The general form of a quadratic equation is y=ax2+bx+c. For the given parabola y=x2, we can see that a=1, b=0, and c 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+c is x=b2a. We will use this formula to find the axis of symmetry for the given parabola.
  3. Substitute Values: Substitute the values of a and b into the formula for the axis of symmetry: x=b2a. Here, a=1 and b=0, so x=021.
  4. Perform Calculation: Perform the calculation: x=021 simplifies to x=0.So, the axis of symmetry is at x=0.
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About Worksheet

Algebra 2
Quadratic Functions

To identify the axis of symmetry of a quadratic function from its equation ax2+bx+c, use the formula x=-b2a. 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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