Question

What could be the possible value of 'y' after the intersection of points y= -x² + 3 and y= x² - 5

• A. \(\sqrt{2}\)
• B. 3/2
• C. 4
• D. \(\sqrt{8}\)
• E. -1

Hint:

When finding the intersection of two functions, after setting them equal and solving for x, remember to substitute the x-value back into one of the original equations to find the corresponding y-value. It's a good practice to check your answer by substituting into the other equation as well to ensure accuracy.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
The intersection points of two graphs are the points (x, y) that satisfy both equations simultaneously. To find these points, we can set the expressions for y equal to each other.
Step 2: Key Formula or Approach:
Given the two equations:
1) \(y = -x^2 + 3\)
2) \(y = x^2 - 5\)
At the point of intersection, the y-values are the same. Therefore, we can equate the right-hand sides of the equations to solve for the x-coordinate of the intersection.
Step 3: Detailed Explanation:
Set the two expressions for y equal to each other:
\[ -x^2 + 3 = x^2 - 5 \] Now, solve this equation for x. Rearrange the terms to group the \(x^2\) terms on one side and the constants on the other.
\[ 3 + 5 = x^2 + x^2 \] \[ 8 = 2x^2 \] \[ x^2 = 4 \] Taking the square root of both sides gives two possible values for x:
\[ x = 2 \quad \text{or} \quad x = -2 \] The question asks for the possible value of 'y'. To find the y-value, substitute either of these x-values back into one of the original equations. Let's use the second equation, \(y = x^2 - 5\).
For \(x = 2\):
\[ y = (2)^2 - 5 = 4 - 5 = -1 \] For \(x = -2\):
\[ y = (-2)^2 - 5 = 4 - 5 = -1 \] In both cases, the y-value at the intersection points is -1. Therefore, the only possible value for 'y' is -1.
Step 4: Final Answer:
The possible value of 'y' at the intersection points is -1.