1. For the function $$ f(x)=2 x^{2}-12 x+13 $$, answer the following. a) Determine the vertex of the quadratic. Your answer should be a coordinate point.

Question

UpStudy AI · Accepted Answer

1. The function is given by
   $$
   f(x) = 2x^2 - 12x + 13.
   $$

2. The $$ x $$-coordinate of the vertex for a quadratic function $$ ax^2+bx+c $$ is calculated as
   $$
   x = -\frac{b}{2a}.
   $$
   For this function, $$ a = 2 $$ and $$ b = -12 $$. Thus,
   $$
   x = -\frac{-12}{2 \cdot 2} = \frac{12}{4} = 3.
   $$

3. To find the $$ y $$-coordinate of the vertex, substitute $$ x = 3 $$ into the function:
   $$
   f(3) = 2(3)^2 - 12(3) + 13.
   $$
   Calculate step by step:
   $$
   f(3) = 2 \cdot 9 - 36 + 13 = 18 - 36 + 13 = -5.
   $$

4. Therefore, the vertex of the quadratic function is:
   $$
   (3, -5).
   $$
The vertex of the quadratic function $$ f(x) = 2x^2 - 12x + 13 $$ is at the point $$ (3, -5) $$.

1. For the function \( f(x)=2 x^{2}-12 x+13 \), answer the following. a) Determine the vertex of the quadratic. Your answer should be a coordinate point.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Algebra Questions