Find the equation of the axis of symmetry for the parabola y = x^2 − 4 . Simplify any numbers and write them as proper fractions, improper fractions, or integers. _____

Identify Coefficients: Identify the coefficients of the quadratic equation. The given parabola is y = x^2 − 4, which can be compared to the standard form y = ax^2 + bx + c. Here, a = 1, b = 0, and c = -4.Use Axis Formula: Use the formula for the axis of symmetry. The axis of symmetry for a parabola in the form y = ax^2 + bx + c is given by the formula x = -b/(2a).Substitute Values: Substitute the values of a and b into the formula. Substitute a = 1 and b = 0 into the formula x = -b/(2a) to find the axis of symmetry. x = -0/(2 × 1) x = 0Write Equation: Write the equation of the axis of symmetry. The axis of symmetry is a vertical line passing through the x-coordinate found in Step 3. Therefore, the equation of the axis of symmetry is x = 0.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the equation of the axis of symmetry for the parabola $y = x^2 - 4$ . $\newline$ Simplify any numbers and write them as proper fractions, improper fractions, or integers. $\newline$ _____

View step-by-step help

Home

Math Problems

Algebra 2

Characteristics of quadratic functions: equations

Full solution

Q. Find the equation of the axis of symmetry for the parabola

y = x^2 - 4

\newline

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

\newline

_____

Identify Coefficients: Identify the coefficients of the quadratic equation. $\newline$ The given parabola is $y = x^2 - 4$ , which can be compared to the standard form $y = ax^2 + bx + c$ . $\newline$ Here, $a = 1$ , $b = 0$ , and $c = -4$ .
Use Axis Formula: Use the formula for the axis of symmetry. $\newline$ The axis of symmetry for a parabola in the form $y = ax^2 + bx + c$ is given by the formula $x = -\frac{b}{2a}$ .
Substitute Values: Substitute the values of $a$ and $b$ into the formula. $\newline$ Substitute $a = 1$ and $b = 0$ into the formula $x = -\frac{b}{2a}$ to find the axis of symmetry. $\newline$ $x = -\frac{0}{2 \times 1}$ $\newline$ $x = 0$
Write Equation: Write the equation of the axis of symmetry. $\newline$ The axis of symmetry is a vertical line passing through the $x$ -coordinate found in Step $3$ . $\newline$ Therefore, the equation of the axis of symmetry is $x = 0$ .