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

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Answer 1 · 2018-04-05T09:30:10

Axis of symmetry formula

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

$x = \frac{- b}{2 a}$ $x=(-b)/(2a)$

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

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

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

So, to determine the axis of symmetry:

$x = \frac{- b}{2 a}$ $x=(-b)/(2a)$

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

$x = 3$ $x=3$

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

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

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

y = $42$ $42$

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

How do you find the axis of symmetry and vertex point of the function: y=−4x2+24x+6y= -4x^2+24x+6?