Equations in Two Variables Quick Check

Question

5 of 55 of 5 Items

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

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

(−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
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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 the \( x \)-value of each ordered pair into the equation and check if the resulting \( y \)-value matches the given \( y \)-value in the pair.

1. For \( (1, 5) \): \[ y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match \( 5 \).

2. For \( (-1, 3) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This matches \( 3 \).

3. For \( (-1, 5) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match \( 5 \).

4. For \( (-1, 43) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match \( 43 \).

The only ordered pair that is part of the solution set for the equation \( y = 5x^2 - 2 \) is \((-1, 3)\).