Question

how do you find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y= -2x^2+6x-1

Answer 1

Answer:

The vertex is: $(\frac{3}{2},\ \frac{7}{2})$

The axis of symmetry is:

$x=\frac{3}{2}$

Step-by-step explanation:

For a quadratic equation of the form:

$y=ax^2 + bx +c$

The vertex of the parabola will be the point: $(-\frac{b}{2a},\ f(-\frac{b}{2a}))$

In this case we have the following equation:

$y= -2x^2+6x-1$

Note that:

$a=-2\\b=6\\c=-1$

Then the x coordinate of the vertex is:

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

$x=-\frac{6}{2(-2)}$

$x=\frac{3}{2}$

Then the y coordinate of the vertex is:

$y= -2(\frac{3}{2})^2+6(\frac{3}{2})-1$

$y=\frac{7}{2}$

The vertex is: $(\frac{3}{2},\ \frac{7}{2})$

For a quadratic function the axis of symmetry is always a vertical line that passes through the vertex of the function.

Then the axis of symmetry is:

$x=\frac{3}{2}$