Find the equation of the axis of symmetry for the parabola y=x2−4x−2. Simplify any numbers and write them as proper fractions, improper fractions, or integers._____
Q. Find the equation of the axis of symmetry for the parabola y=x2−4x−2. Simplify any numbers and write them as proper fractions, improper fractions, or integers._____
Identify Coefficients: Identify the coefficients of the quadratic equation.The quadratic equation is given in the form y=ax2+bx+c. For the parabola y=x2−4x−2, we can identify the coefficients as follows:a=1 (coefficient of x2)b=−4 (coefficient of x)c=−2 (constant term)
Use Axis of Symmetry Formula: Use the formula for the axis of symmetry.The axis of symmetry for a parabola given by the equation y=ax2+bx+c is x=−2ab. We will substitute the values of a and b into this formula to find the axis of symmetry.
Substitute Values into Formula: Substitute the values of a and b into the formula.Using the values from Step 1, we have:a=1b=−4Now, substitute these values into the formula x=−b/(2a):x=−(−4)/(2⋅1)x=4/2x=2
Write Equation of Axis: Write the equation of the axis of symmetry.The axis of symmetry is a vertical line, so its equation is of the form x=constant. From Step 3, we found that the constant is 2. Therefore, the equation of the axis of symmetry is:x=2
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