Identify The `Y`-Intercept Of A Quadratic Functions From Equation Worksheets [PDF]: Algebra 2 Math

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.

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 = x^2

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Simplify any numbers and write them as proper fractions, improper fractions, or integers.

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Solution:

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.
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.
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 $x = -\frac{0}{2\cdot 1}$ .
Perform Calculation: Perform the calculation: $x = -\frac{0}{2\cdot 1}$ simplifies to $x = 0$ . $\newline$ So, the axis of symmetry is at $x = 0$ .