consider the quadratic function: $f(x)=x^{2}-8x - 9$. what is the vertex of the function? vertex…
consider the quadratic function: $f(x)=x^{2}-8x - 9$. what is the vertex of the function? vertex: $(\frac{-b}{2a},f(\frac{-b}{2a}))$
Answer
Explanation:
Step1: Identify coefficients
For the quadratic function $f(x)=x^{2}-8x - 9$, where $a = 1$, $b=-8$, $c=-9$.
Step2: Calculate x - coordinate of vertex
Using the formula $x=\frac{-b}{2a}$, substitute $a = 1$ and $b=-8$. Then $x=\frac{-(-8)}{2\times1}=\frac{8}{2}=4$.
Step3: Calculate y - coordinate of vertex
Substitute $x = 4$ into the function $f(x)=x^{2}-8x - 9$. So $y=f(4)=4^{2}-8\times4 - 9=16-32 - 9=-25$.
Answer:
$(4,-25)$