If \(y = x^{2} - 6x + 11\) is written in the form \(y = a(x - h)^{2} + k\), find the value of \((a + h + k)\).
Question 1 Report
If \(y = x^{2} - 6x + 11\) is written in the form \(y = a(x - h)^{2} + k\), find the value of \((a + h + k)\).
Answer Details
We can start by completing the square to rewrite the quadratic equation in the form given.
\begin{align*}
y &= x^{2} - 6x + 11\\
&= (x^{2} - 6x + 9) + 2\\
&= (x - 3)^{2} + 2
\end{align*}
Now we can see that the equation is in the desired form, with \(a = 1\), \(h = 3\), and \(k = 2\). Therefore,
\begin{align*}
(a + h + k) &= (1 + 3 + 2)\\
&= 6
\end{align*}
So the value of \((a + h + k)\) is 6.
Download The App On Google Playstore
Everything you need to excel in your exams
Personalized AI Learning Chat Assistant
200,000+ Exam Questions Across IGCSE, JAMB, WAEC & NECO
Over 3,900 Lesson Notes
Offline Support - Learn Anytime, Anywhere
Green Bridge Timetable
Literature Summaries & Potential Questions
Track Your Performance & Progress
In-depth Explanations for Comprehensive Learning