Additional Concepts
Determine the direction in which the parabola opens, and the vertex.
-$$y = x ^ { 2 } - 6 x + 5$$
A) Opens upward; $( 3 , - 4 )$
B) Opens upward; $( - 3 , - 4 )$
C) Opens to the right; $( - 4,3 )$
D) Opens to the right; $( - 4 , - 3 )$

Question

Quizplus · Accepted Answer

To determine the direction of the parabola, we look at the coefficient of the squared term. In this case, the coefficient is positive (1), so the parabola opens upward.

To find the vertex, we can use the formula:

$$ \left( \frac{-b}{2a}, f \left( \frac{-b}{2a} \right) \right) $$

where a is the coefficient of the squared term, b is the coefficient of the linear term, and f is the function itself.

Plugging in the values from the given equation, we get:

$$ \left( \frac{-(-6)}{2(1)}, f \left( \frac{-(-6)}{2(1)} \right) \right) $$
$$ \left( 3, f(3) \right) $$
$$ \left( 3, (3)^2 - 6(3) + 5 \right) $$
$$ \left( 3,-4 \right) $$

Therefore, the correct answer is A.

Additional Concepts Determine the Direction in Which the Parabola Opens y=x2−6x+5y = x ^ { 2 } - 6 x + 5y=x2−6x+5

Additional Concepts
Determine the Direction in Which the Parabola Opens $y = x ^ { 2 } - 6 x + 5$