Question

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = 4x2 + 5x – 1.

Answer 1

the axis of symmetry for a quadratic function is x=-b/2a
in this case, b=5, a=4, so the line of symmetry is x=-5/8
find out the value of y when x=-5/8: y=4(-5/8)² +5(-5/8)-1=-41/8
so the vertex is at (-5/8, -41/8)
double check my calculation please.

Answer 2

Answer:

Vertex:

          $(-0.625,-2.563)$

Axis of symmetry:

               $x=-0.625$

Step-by-step explanation:

The function is given by the equation:

$y=4x^2+5x-1$

In general for any quadratic equation of the type:

$y=ax^2+bx+c$

The coordinate of the vertex is: (h,k)

where

$h=\dfrac{-b}{2a}$

and

$k=\dfrac{-(b^2-4ac)}{4a}$

and the equation of axis of symmetry is:

$x=h$

Here we have:

$a=4,\ b=5\ and\ c=-1$

i.e.

$h=\dfrac{-(5)}{2\times 4}\\\\h=\dfrac{-5}{8}=-0.625$

and

$k=\dfrac{-(5^2-4\times 4\times (-1)}{4\times 4}\\\\\\k=\dfrac{-(25+16)}{16}\\\\k=\dfrac{-41}{16}=-2.563$

Hence, the vertex is:

                   $(-0.625,-2.563)$

and the axis of symmetry is given by:

                  $x=-0.625$