Question 1

Which of the following is the correct procedure to find the x-intercept(s) of the graph of an equation?

Accepted Answer

Let $$y = 0 in $$the equation and solve for $$x.$$

Question 2

Given the equation $$y = 2x + 5$$, what is the y-intercept of its graph?

Accepted Answer

$$(0, 5)$$

Question 3

A chemical reaction's rate is modeled by $$y = -3x + 12. $$What does the x-intercept represent in this context?

Accepted Answer

The time when the reaction rate is zero.

Question 4

Which of the following equations is symmetric with respect to the y-axis?

Accepted Answer

$$y = x^2$

Question 5

If a point $$(x, y) is $$reflected over the x-axis, what are the coordinates of its image?

Accepted Answer

$$(x, -y)$$

Question 6

Which test would you use to determine if the equation $$x^2$$ + $$y^2 = 16$ is symmetric with respect to the origin?

Accepted Answer

Replace $$x by$$ $$-x$$ and $$y by$$ $$-y$$ and check if the equation is unchanged.

Question 7

A bridge is modeled by the equation $$y = -0.5x^2$ + 4. $$What is the maximum height of the bridge above the river?

Accepted Answer

$$4$$

Question 8

Which of the following points is the symmetric of $$(3, 2)$$ with respect to the origin?

Accepted Answer

$$(-3, -2)$$

Question 9

Given the equation $$y = x^2$ - 4$$, what are the x-intercepts?

Accepted Answer

$$(2, 0)$$ and $$(-2, 0)$$

Question 10

A company’s profit is modeled by $$y = 5x - 20. $$What does the y-intercept represent in this context?

Accepted Answer

The profit when no units are sold.

Question 11

Which of the following equations is symmetric with respect to the x-axis?

Accepted Answer

$$y^2 = x$

Question 12

If the equation $$y = f(x) is $$symmetric with respect to the y-axis, which of the following must be true?

Accepted Answer

$$f(-x) = f(x)$$ for all x$

Question 13

A circle is centered at $$(2, -3)$$ and passes through the point $$(5, 1). $$What is the equation of the circle?

Accepted Answer

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

Question 14

Which of the following best describes the symmetry of the graph of $$y = x^2$?

Accepted Answer

Symmetric with respect to the y-axis

Question 15

A medical researcher models the spread of a virus with $$y = 100e$$^{-0.2x}$$. What does the y-intercept represent?

Accepted Answer

The initial number of cases

Question 16

Which of the following equations is symmetric with respect to both axes and the origin?

Accepted Answer

$$x^2$$ + $$y^2 = 1$

Question 17

If a point $$(a, b) is $$reflected over the y-axis, what are the coordinates of its image?

Accepted Answer

$$(-a, b)$$

Question 18

Which of the following is the correct test for symmetry with respect to the x-axis for an equation in $$x$$ and $$y$$?

Accepted Answer

Replace $$y by$$ $$-y$$ and check if the equation is unchanged.

Question 19

A parabola opens upward and passes through the points $$(-2, 4)$$, $$(0, 0)$$, and $$(2, 4). $$What is its equation?

Accepted Answer

$$y = x^2$

Graphs of Equations in Two Variables: Intercepts and Symmetry

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