Question 1

Given the linear function $$f(x) = -3x + 7$$, what is the average rate of change of $$f(x)$$ between any two points?

Accepted Answer

$$-3$$

Question 2

A company purchases a computer for $$3000 and depreciates it linearly to 0$ over 3$ years. What is the slope of the linear depreciation model V(x$$)$$, where x$ is the age in years?

Accepted Answer

$$-1000$$

Question 3

Suppose the supply and demand for T-shirts at a concert are given by $$S(p) = 50p$$ and $$D(p) = 1200 - 25p. $$What is the equilibrium price?

Accepted Answer

$$p = 24$$

Question 4

Which of the following best describes the relationship between drilling depth and drilling time based on the scatter plot and table provided?

Accepted Answer

There is a positive linear relationship.

Question 5

Given the quadratic function $$f(x) = 2x^2$ - 6x + 4$$, what is the $$x-$$coordinate of the vertex?

Accepted Answer

$$x = 1.5$$

Question 6

Which of the following is the correct vertex form for the quadratic function $$f(x) = x^2$ + 6x + 5$$?

Accepted Answer

$$f(x) = (x + 3)^2$ - 4$$

Question 7

If the discriminant $$b^2 - 4ac$ of a quadratic equation is negative, what does this indicate about the graph of the quadratic function?

Accepted Answer

There are no real $$x-$$intercepts.

Question 8

A quadratic function $$f(x) = ax^2$ + bx + c$$ opens downward and has its vertex at $$(2, 5). $$Which of the following statements must be true?

Accepted Answer

$$a \u003c 0$$

Question 9

A company’s revenue $$R as a $$function of price $$p is $$given by $$R(p) = -150p^2$ + 21,000p. $$What price maximizes the revenue?

Accepted Answer

$$p = 70$$

Question 10

Which transformation will change the graph of $$f(x) = x^2$ to f(x) = (x$$ - $$2)^2 + 3$?

Accepted Answer

Shift right 2 units and up 3 units.

Question 11

Given the equation $$4x^2 - 12x + 9 = 0$, what is the nature of its solutions?

Accepted Answer

One real solution (double root)

Question 12

If a quadratic function models the height $$h (in $$meters) of a projectile as $$h(x) = -5x^2$ + 20x + 50$$, what is the maximum height reached by the projectile?

Accepted Answer

$$70$$ meters

Question 13

Which of the following scatter plots best represents a quadratic relationship with $$a \u003e 0$$?

Accepted Answer

A plot where the points form a U-shaped pattern opening upwards.

Question 14

Given the 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 15

A quadratic equation $$x^4$$ - $$5x^2 + 6 = 0$ is quadratic in form. What substitution can be used to solve it?

Accepted Answer

Let $$u = x^2$

Question 16

If the axis of symmetry of a parabola is $$x = -2$$ and its vertex is $$(-2, 5)$$, which of the following could be its equation?

Accepted Answer

$$f(x) = a(x + 2)^2$ + 5$$

Question 17

Which of the following best describes the effect of increasing $$|a| in $$the quadratic function $$f(x) = a x^2$?

Accepted Answer

The parabola becomes narrower.

Question 18

Given the quadratic function $$f(x) = -2x^2$ + 8x - 6$$, over which interval is the function increasing?

Accepted Answer

$$(-\infty, 2)$$

Question 19

A suspension bridge cable is modeled by $$y = 0.001x^2$, where x$ is the distance from the center. How high is the cable at x = 100$ meters from the center?

Accepted Answer

$$10$$ meters

Linear and Quadratic Functions: Properties, Models, and Applications

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