Question

consider the quadratic function F(x)=x^2-6x-7the vertex is_______its largest x intercept is x= ________its y intercept is y=_____

Answer 1

Given a equation:

`\begin{gathered} f(x)=ax^2+bx+c \\ \text{the vertex, V(h,k) is:} \\ h=(-b)/(2a) \\ k=f(h) \end{gathered}`

For:

`\begin{gathered} F(x)=x^2-6x-7 \\ a=1 \\ b=-6 \\ c=-7 \\ h=(-(-6))/(2(1))=(6)/(2)=3 \\ k=F(h)=(3)^2-6(3)-7=9-18-7=-16 \end{gathered}`

The vertex is (3,-16)

In order to find the x-intercepts, evaluate the function for F(x) = 0

`\begin{gathered} F(x)=0 \\ x^2-6x-7=0 \\ \text{Factor:} \\ (x-7)(x+1)=0 \\ x=7 \\ or \\ x=-1 \end{gathered}`

x-intercept: (7,0) and (-1,0)

In order to find the y-intercept, evaluate the function for x = 0:

`\begin{gathered} F(0)=(0)^2-6(0)-7 \\ F(0)=-7 \end{gathered}`

y-intercept: (0,-7)