Questions: Use the graph of the quadratic function f to determine the solution. (a) Solve f(x)>0. (b) Solve f(x) ≤ 0. (a) The solution to f(x)>0 is (-∞,-8) ∪(3, ∞). (Type your answer in interval notation.) (b) The solution to f(x) ≤ 0 is . (Type your answer in interval notation.)

Use the graph of the quadratic function f to determine the solution.
(a) Solve f(x)>0.
(b) Solve f(x) ≤ 0.
(a) The solution to f(x)>0 is (-∞,-8) ∪(3, ∞).
(Type your answer in interval notation.)
(b) The solution to f(x) ≤ 0 is .
(Type your answer in interval notation.)

Transcript text: Use the graph of the quadratic function $f$ to determine the solution. (a) Solve $f(x)>0$. (b) Solve $f(x) \leq 0$. (a) The solution to $f(x)>0$ is $(-\infty,-8) \cup(3, \infty)$. (Type your answer in interval notation.) (b) The solution to $f(x) \leq 0$ is $\square$ . (Type your answer in interval notation.)

Solution

Solution Steps

Step 1: Identify the x-intercepts

The graph of the quadratic function intersects the x-axis at \( x = -8 \) and \( x = 3 \).

Step 2: Determine the intervals where \( f(x) > 0 \)

The function \( f(x) \) is greater than 0 when the graph is above the x-axis. This occurs in the intervals \( (-\infty, -8) \) and \( (3, \infty) \).

Step 3: Determine the intervals where \( f(x) \leq 0 \)

The function \( f(x) \) is less than or equal to 0 when the graph is on or below the x-axis. This occurs in the interval \( [-8, 3] \).

Final Answer

(a) The solution to \( f(x) > 0 \) is \( (-\infty, -8) \cup (3, \infty) \).

(b) The solution to \( f(x) \leq 0 \) is \( [-8, 3] \).

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!