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What are the zeros of the quadratic function $f(x) = 3x^2 + 11x - 4$?

What are the x-intercepts of the graph of the equation $y = 4x^2 - 9$?

Which statement best describes the relationship between any pair of x- and y-values that satisfy the equation $y - 2 = x^2$?

Suppose Clare and Lin throw stones into a lake. To determine whose stone hit the water first, what information is needed?

Consider the quadratic equation $y = a(x - b)(x - c)$. Which statement about the equation is always true?

Consider the expression $-2x^2 - 3x + 4$. Which statement about this expression is true?

Clare’s stone reached its maximum height 1.4 seconds after it was tossed. Without additional information, what can NOT be determined?

Which of the following functions has a minimum value of -4?

Clare's stone is tossed and its height can be modeled over time. If you knew the maximum height of Clare's stone, what can you determine?

Jessica was asked to find the minimum value of the quadratic expression $2x^2 - 12x + 17$ by completing the square. What is the minimum value?

Suppose Clare's stone was released and achieved a maximum height. What additional piece of information can help calculate the time when Clare’s stone hit the water?

The distance, d, a car travels at a speed, s, for a time, t, is given by $d = st$. If the speed increases linearly with time, described by $s = 2t + 5$, what type of function describes the distance traveled as a function of time?

A company's profit, P, is modeled by $P(x) = -x^2 + 10x - 9$, where x is the number of units sold. What sales level, x, maximizes the company's profit?

Given the data table with x and f(x) values, which statement best describes the behavior of f(x) as x increases from 0 to 4?

Given the quadratic function $g(x) = (x + 4)^2 + 7$, what effect does shifting the graph 6 units down have on the vertex?

If a parabola has an x-intercept of -4 and a y-intercept of 16, which quadratic function could represent this parabola?

Which characteristic is consistent with a graph of a quadratic function that has a minimum point located at (-3, 3)?

Which statement accurately interprets the graph of the function $f(x) = 0.2(x^2 - 4x - 5)$?

A scientist models phosphorous levels in soil using a function where the input is depth in feet. If 'x' represents the depth below the surface, which domain is most appropriate for this model, assuming the scientist only measures up to 5 feet deep?

If a chief financial officer uses a function to model the projected net profit based on the number of proposed stores (up to 11), what is the most likely practical domain for this function?

Consider a quadratic function modeling profit based that is based on the number of items sold. What does the vertex of the function represent in this context?

Jessica attempted to complete the square for the expression $2x^2 - 12x + 17$. Her steps are shown below:

Step 1: $2(x^2 - 6x) + 17$ Step 2: $2(x^2 - 6x + 9 - 9) + 17$ Step 3: $2(x^2 - 6x + 9) - 9 + 17$ Step 4: $2(x - 3)^2 + 8$

Her teacher told her that one of her steps was wrong. Identify the incorrect step and explain why it is incorrect.

Trevor wants to prove the polynomial identity that begins as $(x + a)(x + b)$. What is the final form of this polynomial after the binomials are multiplied and simplified?

Which of the following equations correctly represents the process of completing the square for the equation $x^2 + 6x = 7$?

Consider the equation $x^2 - 12x = -20$. After completing the square, which of the following represents the solution(s) for x?

Solve $9x^2 + 12x + 5 = 10$ by completing the square. Which of the following represents the correct solution(s) for x?

A theater's weekly profit, $P$, from a comedy show depends on the ticket price, $t$. The equation relating profit and ticket price is not fully provided, but suppose the theater wants to determine the ticket prices at which they would earn $1,500 in profit. Which general approach should they take?

Consider the equation $x + 6 = x^2$. To solve this equation. Which of the following is the correct next step?

If $f(x) = 4x^2 - 3x + 7$, what is the value of $f(-2)$?

Given a function's graph, where the plotted line exists between x = -1 and x = 11 inclusive, but only for real number values, what is the domain of the function?

A ball is launched upwards from an 80-foot building. The trajectory is modeled by a function. Considering the physical constraints, what is the most appropriate domain for this function?

A diver jumps from a 10-foot board, with height modeled by $h = t^2 - 8t + 10$. What is the minimum height the diver reaches?

The height of a baseball is given by $h(t) = -16t^2 + 80t + 3$. How long does it take for the ball to reach its maximum height?

Which graph represents the equation $y = x^2 + 4x - 5$?

What is the equation of the quadratic function that passes through the points (0, −1), (1, 0), and (2, −3)?

Which of the following describes a city population that is increasing as a linear function of time?

Identify the situation that demonstrates a non-linear population change over time.