Questions: f(x)=x^2+2 g(x)=-x+8

Transcript text: \[ \left\{\begin{array}{l} f(x)=x^{2}+2 \\ g(x)=-x+8 \end{array}\right. \]

Solution

Solution Steps

Step 1: Set the Functions Equal

To find the points of intersection of the functions \( f(x) = x^2 + 2 \) and \( g(x) = -x + 8 \), we set them equal to each other: \[ x^2 + 2 = -x + 8 \]

Step 2: Solve for \( x \)

Rearranging the equation gives: \[ x^2 + x - 6 = 0 \] Factoring or using the quadratic formula, we find the solutions: \[ x = -3 \quad \text{and} \quad x = 2 \]

Step 3: Find Corresponding \( y \)-Values

Substituting \( x = -3 \) into \( f(x) \): \[ f(-3) = (-3)^2 + 2 = 9 + 2 = 11 \] Substituting \( x = 2 \) into \( f(x) \): \[ f(2) = (2)^2 + 2 = 4 + 2 = 6 \]

Final Answer

The points of intersection are: \[ \boxed{(-3, 11) \text{ and } (2, 6)} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

Next >