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 passes through all four quadrants.
Which of the following ordered pairs is part of the solution set for the equation y=5x2−2 ?
(1 point)
Responses
(−1,3)
left parenthesis negative 1 comma 3 right parenthesis
(1,5)
left parenthesis 1 comma 5 right parenthesis
(−1,5)
left parenthesis negative 1 comma 5 right parenthesis
(−1,43)
To determine which ordered pairs are part of the solution set for the equation y=5x^2−2, we can substitute the x and y values into the equation and solve for y.
Let's check each option:
1) (-1,3)
y=5(-1)^2-2
y=5(1)-2
y=5-2
y=3
The equation is satisfied, so (-1,3) is a solution.
2) (1,5)
y=5(1)^2-2
y=5(1)-2
y=5-2
y=3
The equation is not satisfied, so (1,5) is not a solution.
3) (-1,5)
y=5(-1)^2-2
y=5(1)-2
y=5-2
y=3
The equation is not satisfied, so (-1,5) is not a solution.
4) (-1,43)
y=5(-1)^2-2
y=5(1)-2
y=5-2
y=3
The equation is not satisfied, so (-1,43) is not a solution.
Therefore, the only ordered pair that is part of the solution set for the equation y=5x^2−2 is (-1,3).