# How do you find the axis of symmetry and vertex point of the function: y= -4x^2+24x+6?

Apr 5, 2018

Axis of symmetry formula

#### Explanation:

While there are several ways to find the axis of symmetry, the simplest method here is probably to just the formula,

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

Where we get the $b$ and $a$ values from the general formula,

$y = a {x}^{2} + b x + c$

Substituting your formula into the equation, we can see that:
$a = - 4$
$b = 24$

So, to determine the axis of symmetry:

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

$x = \frac{- \left(24\right)}{2 \left(- 4\right)}$

$x = 3$

The axis of symmetry is the x value of the vertex point. Knowing this, we simply substitute $x = 3$ in your equation:

y = $- 4 {x}^{2} + 24 x + 6$

y = $- 4 {\left(3\right)}^{2} + 24 \left(3\right) + 6$

y = $42$

So, the vertex point will be at $3 , 42$.