Answer:
Axis of symmetry: [tex]x=-\frac{5}{8}[/tex]
Vertex: [tex](-\frac{5}{8},-2\frac{9}{16})[/tex]
Step-by-step explanation:
The given quadratic equation is
[tex]y=4x^2+5x-1[/tex]
By comparing to the general quadratic function; [tex]y=ax^2+bx+c[/tex]
We have a=4,b=5,c=-1
The equation of the axis of symmetry is given by the formula;
[tex]x=-\frac{b}{2a}[/tex]
We got this formula by completing the square on the general quadratic function.
We substitute a=4 and b=5 to obtain;
[tex]x=-\frac{5}{2(4)}[/tex]
[tex]x=-\frac{5}{8}[/tex]
is the axis of symmetry.
To find the y-value of the vertex, we put [tex]x=-\frac{5}{8}[/tex] into the function to obtain;
[tex]y=4(-\frac{5}{8})^2+5(-\frac{5}{8})-1[/tex]
[tex]y=4(-\frac{5}{8})^2+5(-\frac{5}{8})-1[/tex]
[tex]y=-\frac{41}{16}[/tex]
The vertex of the given function is [tex](-\frac{5}{8},-2\frac{9}{16})[/tex]
