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Find the equation of the axis of symmetry for the parabola y=x2−3y = x^2 - 3. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline__\_\_

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Full solution

Q. Find the equation of the axis of symmetry for the parabola y=x2−3y = x^2 - 3. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline__\_\_
  1. Identify Quadratic Equation: The general form of a quadratic equation is y=ax2+bx+cy = ax^2 + bx + c. In the equation y=x2−3y = x^2 - 3, we can see that a=1a = 1, b=0b = 0, and c=−3c = -3.
  2. Find Axis of Symmetry Formula: The 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}. We will use this formula to find the axis of symmetry for the given parabola.
  3. Substitute Values: Substitute the values of aa and bb into the formula. Since a=1a = 1 and b=0b = 0, we have x=−0/(2⋅1)x = -0/(2\cdot1).
  4. Simplify Expression: Simplify the expression. x=−0/2=0x = -0/2 = 0.
  5. Final Axis of Symmetry: The equation of the axis of symmetry is x=0x = 0.

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