QuestionUse 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 $\square$ (Type your answer in interval notation.) (b) The solution to $f(x) \leq 0$ is $\square$ (Type your answer in interval notation.)

Studdy Solution

STEP 1

1. The quadratic function $f(x)$ is represented by a parabola that opens upwards.
2. The x-intercepts of the parabola are at $x = -4$ and $x = 3$ .
3. The parabola is continuous and symmetric about its vertex.

STEP 2

1. Determine the intervals where $f(x) > 0$ .
2. Determine the intervals where $f(x) \leq 0$ .

STEP 3

Identify the regions where the parabola is above the x-axis. Since the parabola opens upwards and the x-intercepts are at $x = -4$ and $x = 3$ , the function $f(x)$ is positive outside these intercepts. Therefore, the intervals where $f(x) > 0$ are:
$(-\infty, -4) \cup (3, \infty)$

STEP 4

Identify the regions where the parabola is on or below the x-axis. This includes the intervals between and including the x-intercepts. Therefore, the intervals where $f(x) \leq 0$ are:
$[-4, 3]$
The solutions are: (a) The solution to $f(x) > 0$ is $(-\infty, -4) \cup (3, \infty)$ . (b) The solution to $f(x) \leq 0$ is $[-4, 3]$ .

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