Find Domain Of A Quadratic Function From Equation Worksheet

Algebra 2
Quadratic Functions

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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?\newliney=x2+8x+16y = x^2 + 8x + 16\newlineChoices:\newline(A) {yy0}\left\{y\mid y \geq 0\right\}\newline(B) {yy0}\left\{y\mid y \leq 0\right\}\newline(C) {yy4}\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.\newlineThe given function is y=x2+8x+16y = x^2 + 8x + 16, which is in the standard form y=ax2+bx+cy = ax^2 + bx + c.
  2. Find vertex x-coordinate: Find the x-coordinate of the vertex.\newlineThe x-coordinate of the vertex of a parabola in the form y=ax2+bx+cy = ax^2 + bx + c is given by b2a-\frac{b}{2a}. Here, a=1a = 1 and b=8b = 8.\newlinex=821=4x = -\frac{8}{2 \cdot 1} = -4.
  3. Find vertex y-coordinate: Find the y-coordinate of the vertex by substituting x=4x = -4 into the equation.y=(4)2+8(4)+16y = (-4)^2 + 8(-4) + 16y=1632+16y = 16 - 32 + 16y=0y = 0
  4. Determine parabola direction: Determine the direction in which the parabola opens.\newlineSince a=1a = 1 and a>0a > 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.\newlineThe vertex is (4,0)(-4, 0), and since the parabola opens upwards, the range of yy values starts at the yy-coordinate of the vertex and goes to infinity.\newlineRange: {y\{ y | y0}y \geq 0 \}
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About Worksheet

Algebra 2
Quadratic Functions

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 \( y = x^2 -10x + 25 \)

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