Question

What is the axis of symmetry and vertex for the graph `y = 2(x – 4)^2 + 7`?

Answer 1

`:. x = 4`

`:. (4,7)`

Explanation:

The answers can be found through the equation itself.

`y = a(x-b)^2+c`

For axis of symmetry, you just need to look at the terms inside the bracket once you have factorized the equation to its basic state.

A.O.S
`=> (x-4)`

`:. x = 4`

For the point of vertex, which can be a minimum point or a maximum point which can be told by the value of `a`

`-a` = maximum point ; `a` = minimum point

The value of `c` in your equation actually represents the `y-`coordinate of your highest/lowest point.

Thus, your `y-`coordinate is `7`

Point of vertex? Combine the value of your axis of symmetry with your `c` value. This is because the axis of symmetry is always in the middle of the curve, therefore it is also the highest/lowest point of your curve.

`:. (4,7)`