Question 1

Given the graph of a quadratic function opening upwards, which of the following best describes the domain of the function in interval notation?

Accepted Answer

$$(-\infty, \infty)$$

Question 2

A parabola opens upwards and its vertex is at $$(1, -4). $$What is the range of this function in interval notation?

Accepted Answer

$$[-4, \infty)$$

Question 3

Which of the following statements is true about the domain of any quadratic function $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

The domain is $$(-\infty, \infty).$$

Question 4

If a quadratic function models the height (in meters) of a ball thrown upward as $$h(t) = -5t^2$ + 20t + 2$$, what is the domain of $$h in $$the context of this real-world scenario?

Accepted Answer

$$[0, t_{impact}]$$

Question 5

Given the function $$f(x) = x^2$ - 4x + 3$$, what is the minimum value of the function and at what $$x$$ does it occur?

Accepted Answer

Minimum value is $$-1 at$$ $$x = 2$$

Question 6

A company models its profit with $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold. What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$18 at$$ $$x = 2$$

Question 7

Which interval notation correctly represents the range of a quadratic function with vertex at $$(3, -2)$$ and opening upwards?

Accepted Answer

$$[-2, \infty)$$

Question 8

If the graph of a quadratic function opens downward and its vertex is at $$(0, 5)$$, what is the range of the function?

Accepted Answer

$$(-\infty, 5]$$

Question 9

Suppose $$f(x) is a $$quadratic function whose graph passes through the points $$(-1, 2)$$, $$(0, 1)$$, and $$(1, 2). $$What is the range of $$f(x)$$?

Accepted Answer

$$[1, \infty)$$

Question 10

A quadratic function $$f(x)$$ has a minimum value at $$x = -3$$ and $$f(-3) = 7. $$Which of the following is the correct range of $$f(x)$$?

Accepted Answer

$$[7, \infty)$$

Question 11

If the domain of a function is $$(-\infty, \infty)$$ and its range is $$[2, \infty)$$, which of the following could be the vertex of its graph?

Accepted Answer

$$(h, 2)$$

Question 12

A quadratic function $$f(x)$$ has its vertex at $$(4, -6)$$ and opens upwards. What is the minimum value of $$f(x)$$?

Accepted Answer

$$-6$$

Question 13

Which of the following best describes the range of a quadratic function that opens downward with vertex at $$(2, 3)$$?

Accepted Answer

$$(-\infty, 3]$$

Question 14

If $$f(x) = x^2$ + 2x + 5$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$4$$

Question 15

A quadratic function $$f(x)$$ has a range of $$[0, \infty). $$Which of the following could be its equation?

Accepted Answer

$$f(x) = (x - 2)^2$

Domain and Range of Functions: College Algebra Study Notes

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