Question

How do you graph the quadratic function and identify the vertex and axis of symmetry for `y=-x^2+4x-2`?

Answer 1

Vertex`->(x,y)=(2,2)`
Axis of symmetry `->x=2`

Explanation:

As the `x^2` part is negative the graph is of general shape `nn`

The axis of symmetry coincides with `x_("vertex")`

`color(blue)("Determine the vertex and axis of symmetry")`

Write as `y=-1(xcolor(red)(-4)x)-2`

`"Axis of symmetry "=x_("vertex")=(-1/2)xx(color(red)(-4)) = +2`

By substitution:

`y_("vertex")=-(2)^2+4(2)-2 = +2`

Vertex`->(x,y)=(2,2)`
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`color(blue)("Determine the y-intercept")`

Consider the given equation:`" "=-x^2+4xcolor(magenta)(-2)`

`y_("intercept")=color(magenta)(-2)`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the x-intercept")`

Using `y=ax^2+bx+c" where "x=(-b+-sqrt(b^2-4ac))/(2a)`

`a=-1"; "b=+4"; "c=-2`

`x=(-4+-sqrt((4)^2-4(-1)(-2)))/(2(-1))`

I will let you finish this bit.