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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

(−1,5)
left parenthesis negative 1 comma 5 right parenthesis

(1,5)
left parenthesis 1 comma 5 right parenthesis

(−1,43)
left parenthesis negative 1 comma 43 right parenthesis

(−1,3)
left parenthesis negative 1 comma 3 right parenthesis
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Answer 1

To determine which ordered pair is part of the solution set for the equation \( y = 5x^2 - 2 \), we can substitute each value of \( x \) from the ordered pairs into the equation and see if the corresponding \( y \) value matches.

1. For \( (-1, 5) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] \( y \neq 5 \), so this pair is not a solution.

2. For \( (1, 5) \): \[ y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] \( y \neq 5 \), so this pair is not a solution.

3. For \( (-1, 43) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] \( y \neq 43 \), so this pair is not a solution.

4. For \( (-1, 3) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] \( y = 3 \), so this pair is a solution.

The correct ordered pair that is part of the solution set for the equation \( y = 5x^2 - 2 \) is:

(-1, 3).