Use the image to answer the question.
A graph shows both the x-axis and y-axis, ranging from negative 10 to 10 in increments of 5. An upward parabola that passes through all four quadrants is depicted.
Which of the following ordered pairs is part of the solution set for the equation y=3x2−4
?
Option #1: (−2,−8)
Option #2: (2,8)
Option #3: (−4,0)
(1 point)
Option #
is part of the solution set for the equation.
To determine which ordered pair is part of the solution set for the equation y=3x^2-4, we need to substitute the x-coordinate into the equation and check if the resulting y-coordinate matches the given equation.
Let's check each option:
Option #1: (-2,-8)
Substituting x=-2 into the equation:
y = 3(-2)^2 - 4
y = 3(4) - 4
y = 12 - 4
y = 8
Therefore, option #1: (-2, -8) is not part of the solution set.
Option #2: (2,8)
Substituting x=2 into the equation:
y = 3(2)^2 - 4
y = 3(4) - 4
y = 12 - 4
y = 8
Therefore, option #2: (2, 8) is part of the solution set.
Option #3: (-4,0)
Substituting x=-4 into the equation:
y = 3(-4)^2 - 4
y = 3(16) - 4
y = 48 - 4
y = 44
Therefore, option #3: (-4, 0) is not part of the solution set.
To summarize, the ordered pair (2, 8) is part of the solution set for the equation y=3x^2-4.
To determine which of the given ordered pairs is part of the solution set for the equation y = 3x^2 - 4, we can substitute the x and y values from each option into the equation and see if it results in a true statement.
Let's start with option #1: (-2, -8)
Substituting x = -2 and y = -8 into the equation:
-8 = 3(-2)^2 - 4
Simplifying:
-8 = 3(4) - 4
-8 = 12 - 4
-8 = 8
The equation is not true, so (-2, -8) is not part of the solution set.
Next, option #2: (2, 8)
Substituting x = 2 and y = 8 into the equation:
8 = 3(2)^2 - 4
Simplifying:
8 = 3(4) - 4
8 = 12 - 4
8 = 8
The equation is true, so (2, 8) is part of the solution set.
Finally, option #3: (-4, 0)
Substituting x = -4 and y = 0 into the equation:
0 = 3(-4)^2 - 4
Simplifying:
0 = 3(16) - 4
0 = 48 - 4
0 = 44
The equation is not true, so (-4, 0) is not part of the solution set.
Therefore, the only ordered pair that is part of the solution set for the equation y = 3x^2 - 4 is option #2: (2, 8).