Question

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

Answer 1

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=(-b)/(2a)`

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

`y = ax^2 + bx + c`

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

So, to determine the axis of symmetry:

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

`x=(-(24))/(2(-4))`

`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 = `-4x^2 + 24x + 6`

y = `-4(3)^2 + 24(3) + 6`

y = `42`

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