Find the equation of the axis of symmetry for the parabola y = x^2 + 6x + 3/4 . Simplify any numbers and write them as proper fractions, improper fractions, or integers. _____

Quadratic Equation Form: 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). First, identify the values of a and b in the given equation y = x^2 + 6x + 3/4. a = 1 (coefficient of x^2) b = 6 (coefficient of x)Identify Values: Now, substitute the values of a and b into the formula for the axis of symmetry. x = -b/(2a) x = -6/(2*1) x = -6/2 x = -3Calculate Axis of Symmetry: The equation of the axis of symmetry is therefore x = -3. This is a vertical line that passes through the vertex of the parabola and divides it into two mirror-image halves.

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 $y = x^2 + 6x + \frac{3}{4}$ . $\newline$ 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 + 6x + \frac{3}{4}

\newline

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

\newline

_____

Quadratic Equation Form: The general form of a quadratic equation is $y = ax^2 + bx + c$ . To find the axis of symmetry, we use the formula $x = -\frac{b}{2a}$ . $\newline$ First, identify the values of $a$ and $b$ in the given equation $y = x^2 + 6x + \frac{3}{4}$ . $\newline$ $a = 1$ (coefficient of $x^2$ ) $\newline$ $b = 6$ (coefficient of $x$ )
Identify Values: Now, substitute the values of $a$ and $b$ into the formula for the axis of symmetry. $x = \frac{-b}{2a}$ $x = \frac{-6}{2\cdot 1}$ $x = \frac{-6}{2}$ $x = -3$
Calculate Axis of Symmetry: The equation of the axis of symmetry is therefore $x = -3$ . This is a vertical line that passes through the vertex of the parabola and divides it into two mirror-image halves.