Question

Find the vertex of the parabola. tell whether the vertex is a maximum or minimum

Answer 1

The vertex of the prabola whose equation is

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

is (h, k), where

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

The vertex is minimum if a has positive value

The vertex is maximum if a has negative value

Since the given equation is

`f(x)=-4x^2+24x+3`

a = -4

b = 24

c = 3

Let us find h

`\begin{gathered} h=(-24)/(2(-4)) \\ h=(-24)/(-8) \\ h=3 \end{gathered}`

Let us use h to find k

`\begin{gathered} k=f(h)=f(3) \\ k=-4(3)^2+24(3)+3 \\ k=-36+72+3 \\ k=39 \end{gathered}`

The vertex of the parabola is (3, 39)

Since a = -4

That means a is negative, then

The vertex is maximum