Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the equation of the axis of symmetry for the parabola y=x2+6y = x^2 + 6. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline_____\_\_\_\_\_

Full solution

Q. Find the equation of the axis of symmetry for the parabola y=x2+6y = x^2 + 6. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline_____\_\_\_\_\_
  1. Identify Coefficients: Identify the coefficients of the quadratic equation.\newlineThe given parabola is y=x2+6y = x^2 + 6, which can be compared to the standard form y=ax2+bx+cy = ax^2 + bx + c.\newlineHere, a=1a = 1, b=0b = 0 (since there is no xx term), and c=6c = 6.
  2. Use Axis of Symmetry Formula: Use the formula for the axis of symmetry.\newlineThe axis of symmetry for a parabola in the form y=ax2+bx+cy = ax^2 + bx + c is given by the formula x=b2ax = -\frac{b}{2a}.
  3. Substitute Values: Substitute the values of aa and bb into the formula.\newlineSubstitute a=1a = 1 and b=0b = 0 into the formula x=b/(2a)x = -b/(2a) to find the axis of symmetry.\newlinex=0/(2×1)x = -0/(2 \times 1)\newlinex=0x = 0
  4. Write Equation: Write the equation of the axis of symmetry.\newlineThe axis of symmetry is a vertical line passing through the xx-coordinate found in Step 33.\newlineTherefore, the equation of the axis of symmetry is x=0x = 0.

More problems from Characteristics of quadratic functions: equations