what is the vertex of the quadratic function $f(x)=(x - 8)(x - 2)$?
what is the vertex of the quadratic function $f(x)=(x - 8)(x - 2)$?
Answer
Explanation:
Step1: Expand the function
[ \begin{align*} f(x)&=(x - 8)(x - 2)\ &=x^{2}-2x-8x + 16\ &=x^{2}-10x + 16 \end{align*} ]
Step2: Use the formula for the x - coordinate of the vertex
For a quadratic function (y = ax^{2}+bx + c), the x - coordinate of the vertex is (x=-\frac{b}{2a}). Here (a = 1), (b=-10), so (x=-\frac{-10}{2\times1}=5).
Step3: Find the y - coordinate of the vertex
Substitute (x = 5) into the function (f(x)=x^{2}-10x + 16). Then (f(5)=5^{2}-10\times5 + 16=25-50 + 16=-9).
Answer:
((5,-9))