Identify The `Y`-Intercept Of A Quadratic Functions From Equation Worksheet

Algebra 2
Quadratic Functions

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How Will This Worksheet on "Identify the `y`-Intercept of a Quadratic Function from Equation" Benefit Your Student's Learning?

  • Reinforces understanding of the `y`-intercept concept in quadratic functions.
  • Develops critical thinking by analyzing quadratic equations to find the `y`-intercept.
  • Strengthens algebraic skills through manipulation of quadratic equations.
  • Enhances graphical interpretation of `y`-intercepts on quadratic function graphs.
  • Applies mathematical concepts to real-world scenarios for practical understanding.
  • Improves mathematical literacy through interpretation and analysis practice.
  • Prepares students for assessments involving quadratic functions and their properties.
  • Encourages self-directed learning and builds confidence in quadratic function comprehension.

How to Identify the `y`-Intercept of a Quadratic Function from Equation?

  • A quadratic equation is typically written in the form: `y=ax^2+bx+cy` where `a, b,` and `c` are constants, and `x` is the variable.
  • The `y`-intercept occurs where `x=0`. To find it, substitute `x = 0` into the equation.
  • Substitute `x=0` into the equation and simplify to find the value of `y`.
  • The resulting value of `y` when `x=0` is the `y`-coordinate where the graph of the quadratic function intersects the `y`-axis, which is the `y`-intercept.

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 `y`-intercept of a quadratic function from its equation, substitute \( x = 0 \) into the equation \( y = ax^2 + bx + c \). This point corresponds to the value of the function when \( x = 0 \). It provides crucial information about the initial value or starting point of the quadratic function on the vertical axis, irrespective of its parabolic shape.

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