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

Apr 16, 2016

The vertex is a coordinate $\left(x , y\right)$ 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.

$x = \frac{- b}{2 a}$
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: $a {x}^{2} + b x + c = 0$ 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.

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

$x = \frac{- 144}{\left(2\right) \left(- 12\right)}$

$x = \frac{- 144}{- 24}$

$x = 6$

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:
$y = - 12 {\left(6\right)}^{2} + 144 \left(6\right) + 2$
$y = 434$

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).