Question

Question

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 negative 1 comma 5 right parenthesis

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

(1,5)
left parenthesis 1 comma 5 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 need to plug in the x-values from each ordered pair into the equation and see if we get the corresponding y-values.

Let's evaluate each option:

1. For \((-1, 3)\): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] The ordered pair \((-1, 3)\) satisfies the equation.

2. For \((-1, 5)\): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] The y-value is 3, not 5. So, \((-1, 5)\) does not satisfy the equation.

3. For \((-1, 43)\): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] The y-value is 3, not 43. So, \((-1, 43)\) does not satisfy the equation.

4. For \((1, 5)\): \[ y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] The y-value is 3, not 5. So, \((1, 5)\) does not satisfy the equation.

Based on the evaluations, the only ordered pair that satisfies the equation \( y = 5x^2 - 2 \) is:

\((-1, 3)\)