# What is the vertex of  y=x^2 - 8x - 3 ?

Jan 1, 2016

The Solution set(or vertex set) is: $S = \left\{4 , - 19\right\}$

#### Explanation:

The general formula for a quadratic function is:
$y = A {x}^{2} + B x + C$

To find the vertex, we apply those formulas:
${x}_{v e r t e x} = - \frac{b}{2 a}$
${y}_{v e r t e x} = - \frac{\triangle}{4 a}$

In this case:
${x}_{v e r t e x} = - \frac{- 8}{2 \cdot 1} = - \left(- 4\right) = 4$ and
${y}_{v e r t e x} = - \frac{{b}^{2} - 4 a c}{4 \cdot 1} = - \frac{64 - 4 \cdot 1 \cdot \left(- 3\right)}{4}$
${y}_{v e r t e x} = - \frac{76}{4} = - 19$

So, the Solution set(or vertex set) is: $S = \left\{4 , - 19\right\}$