# Find Domain Of A Quadratic Function From Equation Worksheet

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The domain of a quadratic function includes all possible x-values that the function can accept. For the equation $$y = ax^2 + bx + c$$, solving for y will always yield a real number. Therefore, the domain of any quadratic function is all real numbers. These worksheets will guide students in identifying the domain of quadratic equations.

Example: What is the domain of $$y = x^2 -10x + 25$$

Algebra 2

## How Will This Worksheet on "Find Domain of a Quadratic Function from Equation" Benefit Your Student's Learning?

• Develops problem-solving skills applicable to different mathematical concepts.
• Enhances understanding of the domain, essential for advanced problems.
• Improves critical thinking by evaluating equation structures and their influence on solutions.
• Helps students clearly express their reasoning and solutions.
• Equips students for higher-level mathematical studies and applications.

## How to Find Domain of a Quadratic Function from Equation?

• Understand that the domain of a quadratic function in the form $$ax^2 + bx + c$$ includes all real numbers since there are no restrictions on $$x$$.
• Represent the domain as $$(-\infty, \infty)$$.

## Solved Example

Q. What is the range of this quadratic function?$\newline$$y = x^2 + 8x + 16$$\newline$Choices:$\newline$(A) $\left\{y\mid y \geq 0\right\}$$\newline$(B) $\left\{y\mid y \leq 0\right\}$$\newline$(C) $\left\{y\mid y \geq -4\right\}$$\newline$(D) all real numbers
Solution:
1. Identify general form: Identify the general form of the quadratic function.$\newline$The given function is $y = x^2 + 8x + 16$, which is in the standard form $y = ax^2 + bx + c$.
2. Find vertex x-coordinate: Find the x-coordinate of the vertex.$\newline$The x-coordinate of the vertex of a parabola in the form $y = ax^2 + bx + c$ is given by $-\frac{b}{2a}$. Here, $a = 1$ and $b = 8$.$\newline$$x = -\frac{8}{2 \cdot 1} = -4$.
3. Find vertex y-coordinate: Find the y-coordinate of the vertex by substituting $x = -4$ into the equation.$y = (-4)^2 + 8(-4) + 16$$y = 16 - 32 + 16$$y = 0$
4. Determine parabola direction: Determine the direction in which the parabola opens.$\newline$Since $a = 1$ and $a > 0$, the parabola opens upwards.
5. Find range of function: Find the range of the function based on the vertex and the direction of the parabola.$\newline$The vertex is $(-4, 0)$, and since the parabola opens upwards, the range of $y$ values starts at the $y$-coordinate of the vertex and goes to infinity.$\newline$Range: $\{ y$ | $y \geq 0 \}$

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