Q: If $$f(x) = x^2$ - 6x + 8$$, which values of $$x$$ satisfy $$f(x) \geq 0$$?

$$x \leq 2$$ \,\text{or}\, x \geq 4$

Q: A quadratic function $$f(x)$$ has zeros at $$x = -1$$ and $$x = 4. $$For which values of $$x is$$ $$f(x) \geq 0$$?

$$x \leq -1$$ \,\text{or}\, x \geq 4$

Q: If $$f(x) = x^2$ + 2x - 8$$, which values of $$x$$ satisfy $$f(x) = 0$$?

$$x = -4$$ \,\text{or}\, x = 2$

Question 1

Given the quadratic function $$f(x) = x^2$ - 4x + 3$$, for which values of $$x is$$ $$f(x) \u003c 0$$?

Accepted Answer

$$1 \u003c x \u003c 3$$

Question 2

If the graph of $$f(x)$$ crosses the $$x-$$axis at $$x = -2$$ and $$x = 5$$, which interval represents where $$f(x) \u003e 0$$?

Accepted Answer

$$x  5$$

Question 3

A projectile is launched and its height (in meters) after $$t$$ seconds is given by $$h(t) = -5t^2$ + 20t + 10. $$For which values of $$t is $$the projectile above ground level ($$h(t) \u003e 0$$)?

Accepted Answer

$$0 \u003c t \u003c 4$$

Question 4

If $$f(x) = x^2$ - 6x + 8$$, which values of $$x$$ satisfy $$f(x) \geq 0$$?

Accepted Answer

$$x \leq 2$$ \,	ext{or}\, x \geq 4$

Question 5

Suppose $$f(x) = -x^2$ + 4x - 3. $$For which values of $$x is$$ $$f(x) \u003c 0$$?

Accepted Answer

$$x  3$$

Question 6

A chemical reaction's rate is modeled by $$R(t) = t^2$ - 6t + 9. $$For which values of $$t is $$the rate zero?

Accepted Answer

$$t = 3$$

Question 7

If the graph of $$f(x) is $$below the $$x-$$axis between $$x = -3$$ and $$x = 2$$, which interval represents $$f(x) \u003c 0$$?

Accepted Answer

$$-3 \u003c x \u003c 2$$

Question 8

A quadratic function $$f(x)$$ has zeros at $$x = -1$$ and $$x = 4. $$For which values of $$x is$$ $$f(x) \geq 0$$?

Accepted Answer

$$x \leq -1$$ \,	ext{or}\, x \geq 4$

Question 9

If $$f(x) = x^2$ + 2x - 8$$, which values of $$x$$ satisfy $$f(x) = 0$$?

Accepted Answer

$$x = -4$$ \,	ext{or}\, x = 2$

Question 10

A medical dosage is modeled by $$D(t) = -2t^2$ + 8t. $$For which values of $$t is $$the dosage positive ($$D(t) \u003e 0$$)?

Accepted Answer

$$0 \u003c t \u003c 4$$

Question 11

If $$f(x) = x^2$ - 2x - 3$$, for which values of $$x is$$ $$f(x) \leq 0$$?

Accepted Answer

$$-1 \leq x \leq 3$$

Question 12

A company's profit is modeled by $$P(x) = -x^2$ + 6x - 8. $$For which values of $$x is $$the profit zero?

Accepted Answer

$$x = 2$$ \,	ext{or}\, x = 4$

Question 13

If $$f(x) = x^2$ - 9$$, for which values of $$x is$$ $$f(x) \u003e 0$$?

Accepted Answer

$$x  3$$

Question 14

A quadratic function $$f(x) is $$above the $$x-$$axis for $$x  5. $$Which interval represents $$f(x) \u003e 0$$?

Accepted Answer

$$x  5$$

Question 15

If $$f(x) = -x^2$ + 2x + 8$$, for which values of $$x is$$ $$f(x) \geq 0$$?

Accepted Answer

$$-2 \leq x \leq 4$$

Question 16

A quadratic function $$f(x)$$ has its graph below the $$x-$$axis for $$x$$ between $$-5$$ and $$2. $$Which interval represents $$f(x) \u003c 0$$?

Accepted Answer

$$-5 \u003c x \u003c 2$$

Question 17

If $$f(x) = x^2$ - 10x + 21$$, for which values of $$x is$$ $$f(x) = 0$$?

Accepted Answer

$$x = 3$$ \,	ext{or}\, x = 7$

Question 18

A quadratic function $$f(x) is $$above the $$x-$$axis for $$x  2. $$Which interval represents $$f(x) \u003e 0$$?

Accepted Answer

$$x  2$$

Step-by-Step Guidance for Solving Quadratic Inequalities from Graphs

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