Find the equation of the axis of symmetry for the parabola y = x^2 + 4x + 3 . Simplify any numbers and write them as proper fractions, improper fractions, or integers. _____

Identify Quadratic Equation: The general form of a quadratic equation is y = ax^2 + bx + c. To find the axis of symmetry, we use the formula x = -b/(2a). For the given parabola y = x^2 + 4x + 3, we can identify a = 1 and b = 4 by comparing it to the general form.Calculate Axis of Symmetry: Now we substitute the values of a and b into the formula for the axis of symmetry. x = -b/(2a) = -4/(2*1) = -4/2 = -2. This calculation gives us the x-coordinate of the vertex of the parabola, which lies on the axis of symmetry.Equation of Axis of Symmetry: The equation of the axis of symmetry is therefore x = -2. This is a vertical line passing through the vertex of the parabola.

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 $y = x^2 + 4x + 3$ . $\newline$ 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 + 4x + 3

\newline

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

\newline

\_\_

Identify Quadratic Equation: The general form of a quadratic equation is $y = ax^2 + bx + c$ . To find the axis of symmetry, we use the formula $x = -\frac{b}{2a}$ . $\newline$ For the given parabola $y = x^2 + 4x + 3$ , we can identify $a = 1$ and $b = 4$ by comparing it to the general form.
Calculate Axis of Symmetry: Now we substitute the values of $a$ and $b$ into the formula for the axis of symmetry. $x = -\frac{b}{2a} = -\frac{4}{2\cdot 1} = -\frac{4}{2} = -2.$ This calculation gives us the $x$ -coordinate of the vertex of the parabola, which lies on the axis of symmetry.
Equation of Axis of Symmetry: The equation of the axis of symmetry is therefore $x = -2$ . This is a vertical line passing through the vertex of the parabola.