Question

What is the vertex form of `y=-12x^2+144x+2`?

Answer 1

The vertex is a coordinate `(x, y)` from which the parabola will represent a maximum or a minimum value depending on whether the parabola is facing up or down.

It's important to know the formula for finding the axis of symmetry for these type of problems.

`x = (-b)/(2a)`
The axis of symmetry is the "point of reflection" for the parabola for the quadratic equation. If you graph the equation, then you will see that from that particular x coordinate, the parabola is basically reflecting th y-coordinates.

Also know that the standard form of a quadratic equation is: `ax^2 + bx + c = 0` where a and b are coefficients and c is a constant.

In this case, the a term is -12, the b term is 144, and the c term is 2.

Substitute these values accordingly to the formula for finding the axis of symmetry.

`x = (-b)/(2a)`

`x = (-144)/((2)(-12))`

`x = (-144)/(-24)`

`x = 6`

This is the x value of the coordinate of the vertex.

To find the y value plug in the x value back to the equation:
`y = -12(6)^2 + 144(6) + 2`
`y = 434`

So our vertex is: (6, 434) graph{-12x^2 + 144x + 2 [-126.6, 157.7, 308.5, 450.7]}

Notice this graph. The parabola is very thin so it is somewhat difficult to exactly decipher the vertex accurately. But it is around
(6, 434).