Answer:
Axis of symmetry: [tex]x=\frac{5}{6}[/tex]
Vertex: [tex](\frac{5}{6} ,\frac{73}{12} )[/tex]
Step-by-step explanation:
Recall that the formula for the axis of symmetry of a quadratic function of the form: [tex]y=a\,x^2+b\,x+c[/tex] is that of a vertical line of the form [tex]x=-\frac{b}{2a}[/tex]
Since for our case, [tex]a=-3, \,and\,\,b=5,[/tex] then the equation for the axis of symmetry is:
[tex]x=-\frac{5}{2(-3)} \\x=\frac{5}{6}[/tex]
The horizontal (x) coordinate for the vertex is therefore 5/6, and the y coordinate can be obtained by replacing 'x" with the value "5/6" in the function's expression:
[tex]y=-3x^2+5x+4\\y=-3(\frac{5}{6} )^2+5(\frac{5}{6} )+4\\y=-\frac{25}{12} +\frac{25}{6} +4\\y=-\frac{25}{12} +\frac{50}{12} +\frac{48}{12} \\y=\frac{73}{12}[/tex]
