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

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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.

Algebra 2

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 $y = x^2$. $\newline$Simplify 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 $y = ax^2 + bx + c$.$\newline$ For the given parabola $y = x^2$, 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 $y = ax^2 + bx + c$ is $x = -\frac{b}{2a}$.$\newline$ We will use this formula to find the axis of symmetry for the given parabola.
3. Substitute Values: Substitute the values of $a$ and $b$ into the formula for the axis of symmetry: $x = -\frac{b}{2a}$.$\newline$ Here, $a = 1$ and $b = 0$, so $x = -\frac{0}{2\cdot 1}$.
4. Perform Calculation: Perform the calculation: $x = -\frac{0}{2\cdot 1}$ simplifies to $x = 0$.$\newline$So, the axis of symmetry is at $x = 0$.

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