# How do you write the quadratic in vertex form given y=-3x^2-24x+7?

May 10, 2015

Coordinates of vertex :

$x = - \frac{b}{2 a} = \frac{24}{-} 6 = - 4$

y = f(-b/2a) = f(-4) = -3(16) - 24(-4) + 7 = -48 + 96 + 7 = 55

Vertex form: $y = - 3. {\left(x + 4\right)}^{2} + 55$

Check:

$D e v e l o p : - 3 {\left(x + 4\right)}^{2} + 55 = - 3. \left({x}^{2} + 8 x + 16\right) + 55$ =
$= - 3 {x}^{2} - 24 x - 48 + 55 = - 3 {x}^{2} - 24 x + 7.$ Correct