Use a graphing calculator or computer to decide which one of the viewing rectangles produces the most appropriate graph of the equation $y = 4 x ^ { 2 } - 12 x + 6$ .
A) $[ 2,10 ]$ by
$[ - 10,10 ]$
B) $[ - 1,4 ]$ by
$[ - 3,20 ]$
C) $[ 5,10 ]$ by
$[ - 10,50 ]$
D) $[ - 10,3 ]$ by
$[ 0,50 ]$
E) $[ - 10,10 ]$ by
$[ - 20,20 ]$

Question

Quizplus · Accepted Answer

The graph of $y = 4x^2 - 12x + 6$ is a parabola opening upwards. The vertex of this parabola, found using the formula $-\frac{b}{2a}$ for $x$, is at $x = \frac{12}{8} = 1.5$. The corresponding $y$ value at the vertex can be calculated by substituting $x = 1.5$ into the equation, yielding $y = 4(1.5)^2 - 12(1.5) + 6 = -3$. Therefore, the most appropriate viewing rectangle would include the vertex and a reasonable range around it to display the parabola's shape effectively. Option B, with the range $[-1,4]$ by $[-3,20]$, covers the vertex and provides a good view of the parabola's curvature and direction, making it the most appropriate choice.

Use a Graphing Calculator or Computer to Decide Which One y=4x2−12x+6y = 4 x ^ { 2 } - 12 x + 6y=4x2−12x+6

Use a Graphing Calculator or Computer to Decide Which One $y = 4 x ^ { 2 } - 12 x + 6$