Question

Find the vertex of the following parabola.f(x) = x² + 3x - 8?+The vertex is(Type an ordered pair, using integers or fractions)

Answer 1

The quadratic function of the form

`f(x)=ax^2+bx+c`

Has a vertex of (h, k) where

`\begin{gathered} h=(-b)/(2a) \\ k=f(h) \end{gathered}`

Since the given function is

`f(x)=x^2+3x-8`

Compare it with the form above to find a, b

`\begin{gathered} a=1 \\ b=3 \end{gathered}`

Substitute them in the rule of h to find it

`\begin{gathered} h=(-3)/(2(1)) \\ h=-(3)/(2) \end{gathered}`

To find k, substitute x by the value of h

`\begin{gathered} k=f(h),h=-(3)/(2) \\ f(-(3)/(2))=(-(3)/(2))^2+3(-(3)/(2))-8 \\ f(-(3)/(2))=(9)/(4)-(9)/(2)-8 \\ f(-(3)/(2))=-(41)/(4) \\ k=-(41)/(4) \end{gathered}`

The vertex of the parabola is

`(-(3)/(2),-(41)/(4))`