Question 1

Which of the following ordered pairs is a solution to the equation $$2x + 3y = 18$$?

Accepted Answer

$$(3, 4)$$

Question 2

What is the $$x-$$intercept of the equation $$2x + 3y = 18$$?

Accepted Answer

$$(9, 0)$$

Question 3

Find the $$y-$$intercept of the equation $$2x + 3y = 18.$$

Accepted Answer

$$(0, 6)$$

Question 4

Which formula correctly gives the distance $$d$$ between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$d = \sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 5

A delivery drone travels from $$(-2, 2) to$$ $$(3, -6). $$What is the distance it travels?

Accepted Answer

$$\sqrt{89}$$

Question 6

What is the midpoint between the points $$(-4, -2)$$ and $$(2, 5)$$?

Accepted Answer

$$(-1, \frac{3}{2})$$

Question 7

Which equation represents a circle with center $$(3, -7)$$ and radius $$5$$?

Accepted Answer

$$(x - 3)^2$ + (y + 7)^2$ = 25$$

Question 8

A company’s profit $$y (in $$thousands of dollars) is modeled by $$y = x^2$ - 9x - 12$$, where $$x is $$the number of units sold (in thousands). What is the profit when $$x = 0$$?

Accepted Answer

$$-12$$

Question 9

Which of the following points lies in Quadrant II of the Cartesian plane?

Accepted Answer

$$(-2, 5)$$

Question 10

Given the equation $$2x + 3y = 18$$, what is the value of $$y$$ when $$x = 5$$?

Accepted Answer

$$y = \frac{8}{3}$$

Question 11

A city park is to be designed in the shape of a circle with center at $$(2, -3)$$ and radius $$7$$ units. Which equation models the park’s boundary?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 49$$

Question 12

Which of the following best describes the $$y-$$intercept of a graph?

Accepted Answer

The point where the graph crosses the $$y-$$axis.

Question 13

If the endpoints of a diameter of a circle are $$(1, 2)$$ and $$(7, 8)$$, what is the center of the circle?

Accepted Answer

$$(4, 5)$$

Question 14

A biologist tracks two tagged animals. One is at $$(2, 3)$$ and the other at $$(8, 11). $$What is the distance between them?

Accepted Answer

$$\sqrt{100} = 10$$

Question 15

Which of the following is NOT a solution to $$y = x^2$ - 9x - 12$$?

Accepted Answer

$$(2, 0)$$

Question 16

A line passes through $$(1, 2)$$ and $$(5, 10). $$What is the midpoint of the segment joining these points?

Accepted Answer

$$(3, 6)$$

Question 17

Which of the following best describes the graph of $$y = x^2$ - 9x - 12$$?

Accepted Answer

A parabola opening upwards

Question 18

If a circle has the equation $$(x + 2)^2$ + (y - 5)^2$ = 36$$, what is its center and radius?

Accepted Answer

Center $$(-2, 5)$$, radius $$6$$

Question 19

Which of the following statements is TRUE about the Cartesian coordinate system?

Accepted Answer

Quadrant II contains points where $$x  0.$$

Chapter 1: Graphs, Functions, and Models – College Algebra Study Notes

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