Find the vertex by using the vertex formula. $$f ( x ) = x ^ { 2 } + 10 x - 6$$
A) $\left( - 5 , \frac { 11 } { 4 } \right)$
B) $( 10 , - 6 )$
C) $( - 5 , - 31 )$
D) $( - 10,6 )$

Question

Quizplus · Accepted Answer

The vertex of a parabola given by $f(x) = ax^2 + bx + c$ can be found using the formula $(- \frac{b}{2a}, f(- \frac{b}{2a}))$. For $f(x) = x^2 + 10x - 6$, $a = 1$, $b = 10$, and $c = -6$. Thus, the x-coordinate of the vertex is $- \frac{10}{2(1)} = -5$. Substituting $x = -5$ into the original equation gives $f(-5) = (-5)^2 + 10(-5) - 6 = 25 - 50 - 6 = -31$. Therefore, the vertex is $(-5, -31)$.

Find the Vertex by Using the Vertex Formula f(x)=x2+10x−6f ( x ) = x ^ { 2 } + 10 x - 6f(x)=x2+10x−6

Find the Vertex by Using the Vertex Formula $f ( x ) = x ^ { 2 } + 10 x - 6$