Question

What is the axis of symmetry and vertex for the graph `y= -4x^2 + 3`?

Answer 1

See explanation

Explanation:

Consider the standard form of `y=ax^2+bx+c`

The y-axis intercept is the constant c which in this case gives `y=3`

As the `bx` term is not 0 (not there) then the graph is symmetrical about the y-axis. Consequently the vertex is actually on the y-axis.

`color(blue)("Axis of symmetry is: "x=0)`
`color(blue)("Vertex "->(x,y)=(0,3)`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Foot Note:")`

As the `ax^2` term is negative the graph form is `nn`

If the `ax^2` term had been positive then in that instance the graph form would be `uu`

As a general rule the axis of symmetry is at `x=(-1/2)xxb/a`

Consider the example of `y=ax^2+bx+c" "->" "y=-2x^2+3x-4`

In this case the axis of symmetry will be at:

`x=(-1/2)xxb/a" "->" "(-1/2)xx3/(-2)" " =" " 3/4`