Question

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of y=4x^2+5x-1

Answer 1

Answer:

Axis of symmetry: $x=-\frac{5}{8}$

Vertex: $(-\frac{5}{8},-2\frac{9}{16})$

Step-by-step explanation:

The given quadratic equation is

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

By comparing to the general quadratic function; $y=ax^2+bx+c$

We have a=4,b=5,c=-1

The equation of the axis of symmetry is given by the formula;

$x=-\frac{b}{2a}$

We got this formula by completing the square on the general quadratic function.

We substitute a=4 and b=5 to obtain;

$x=-\frac{5}{2(4)}$

$x=-\frac{5}{8}$
is the axis of symmetry.

To find the y-value of the vertex, we put $x=-\frac{5}{8}$ into the function to obtain;

$y=4(-\frac{5}{8})^2+5(-\frac{5}{8})-1$

$y=4(-\frac{5}{8})^2+5(-\frac{5}{8})-1$

$y=-\frac{41}{16}$

The vertex of the given function is $(-\frac{5}{8},-2\frac{9}{16})$