Question

Find the axis of symmetry and the vertex of the graph for the quadratic function y=-3x2 + 5x + 4.

Answer 1

Axis of symmetry:
`x=(5)/(6)`

Vertex:
`((5)/(6) ,(73)/(12) )`

Explanation:

Recall that the formula for the axis of symmetry of a quadratic function of the form:
`y=a\,x^2+b\,x+c` is that of a vertical line of the form
`x=-(b)/(2a)`

Since for our case,
`a=-3, \,and\,\,b=5,` then the equation for the axis of symmetry is:

`x=-(5)/(2(-3)) \\x=(5)/(6)`

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:

`y=-3x^2+5x+4\\y=-3((5)/(6) )^2+5((5)/(6) )+4\\y=-(25)/(12) +(25)/(6) +4\\y=-(25)/(12) +(50)/(12) +(48)/(12) \\y=(73)/(12)`