Question

Consider$y=x^2-5x+4$

Write the equation of the axis of symmetry.

Short answer

The equation of the axis of symmetry for the given function is, $\mathit{x}\mathbf{=}\frac{\mathbf{5}}{\mathbf{2}}$.

Step-by-step solution

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, $y=a{x}^2+bx+c$, where, $a\ne 0$ is called the standard form of the quadratic function.

Step 2. Write the axis of symmetry for the function y=ax2+bx+c.

The axis of symmetry for the function $y=a{x}^2+bx+c$is

$x=-\frac{b}{2a}$

Step 3. Write the equation of the axis of symmetry for the function y=x2−5x+4.

Compare the quadratic function, $y=x^2-5x+4$with the standard equation of the quadratic function, $y=a{x}^2+bx+c$.

$a=1,b=-5,c=4$

Substitute, $a=1$and $b=-5$in $x=-\frac{b}{2a}$

$$\begin{gathered} x=-\frac{\left(-5\right)}{2\left(1\right)} \\ x=\frac{5}{2} \end{gathered}$$

Therefore, the equation of the axis of symmetry for the given function is, $x=\frac{5}{2}$.