Question

Given \[y={{x}^{2}}-5x+4\]. How do you write the equation of the axis of symmetry?

Answer 1

Hint: We know that a quadratic equation \[y=a{{x}^{2}}+bx+c\] , the equation of symmetry is \[y=\dfrac{-b}{2a}\]. First of all, we should compare \[y=a{{x}^{2}}+bx+c\] with \[y={{x}^{2}}-5x+4\]. From this, we have to find the values of a, b and c. From this we have to find the value of \[\dfrac{-b}{2a}\]. In this way, we can find the axis of symmetry.

Complete step-by-step answer:
From the question, it is given that \[y={{x}^{2}}-5x+4\] and we have to find the equation of the axis of symmetry.
We know that a quadratic equation \[y=a{{x}^{2}}+bx+c\] , the equation of symmetry is \[y=\dfrac{-b}{2a}\].
Now we have to compare \[y=a{{x}^{2}}+bx+c\] with \[y={{x}^{2}}-5x+4\]. Now we have to compare the both equations, we have to find the values of a, b and c respectively.
So, it is clear that the value of a, b and c are equal to 1, -5 and 4 respectively.
Let us consider
\[\begin{align}
  & a=1....(1) \\
 & b=-5...(2) \\
 & c=4...(3) \\
\end{align}\]
We already know that a quadratic equation \[y=a{{x}^{2}}+bx+c\] , the equation of symmetry is \[y=\dfrac{-b}{2a}\].
Now we have to find the axis of symmetry of \[y={{x}^{2}}-5x+4\].
Now we have to find the value of \[\dfrac{-b}{2a}\].
Let us assume the value of \[\dfrac{-b}{2a}\] is equal to A.
\[\Rightarrow A=\dfrac{-b}{2a}....(4)\]
Let us substitute equation (1), equation (2) and equation (3) in equation (4), then we get
\[\begin{align}
  & \Rightarrow A=\dfrac{-(-5)}{2(1)} \\
 & \Rightarrow A=\dfrac{5}{2}..(5) \\
\end{align}\]
So, it is clear that the equation of symmetry is \[y=\dfrac{5}{2}\].

Note: Students may have a misconception that for a quadratic equation \[y=a{{x}^{2}}+bx+c\] , the equation of symmetry is \[y=\dfrac{b}{2a}\]. But we know that a quadratic equation \[y=a{{x}^{2}}+bx+c\] , the equation of symmetry is \[y=\dfrac{-b}{2a}\]. So, if this misconception is followed, then the final answer may get interrupted.