Chapter 4.4, Problem 2MCQ

To determine

To find: The correct option of the function for the given axis of symmetry.

Answer to Problem 2MCQ

The correct option is B.

Explanation of Solution

Given:

The given axis of symmetry is $x=5$ .

First consider the function $f\left(x\right)=x^2-5x+3$

To convert the above equation in the standard form of parabola the calculation is given as:

  $\begin{array}{c}f\left(x\right)=x^2-5x+\frac{25}{4}-\frac{25}{4}+3\\ ={\left(x-\frac{5}{2}\right)}^2-\frac{13}{4}\end{array}$

The equation of the axis of symmetry of above solved equation is $x=\frac{5}{2}$ .

Further consider the function $f\left(x\right)=x^2-10x+7$ .

To convert the above equation in the standard form of parabola the calculation is given as:

  $\begin{array}{c}f\left(x\right)=x^2-10x+25-25+7\\ ={\left(x-5\right)}^2-18\end{array}$

The equation of the axis of symmetry of above solved equation is $x=5$ .

As the above equation is required answer no need to check further.

Therefore, the correct option is B.