The vertex of the parabola x − 2 = -3(y + 1)2 is:
A. (-2,1)
Incorrect. Remember, in the standard form, the vertex is at (h,k). Pay close attention to the signs of h and k in the standard form.
B. (-2,-1)
Incorrect. Remember, in the standard form, the vertex is at (h,k). Pay close attention to the signs of h and k.
C. (-1,2)
Incorrect. This is a sideways parabola shifted 2 units right and 1 unit down.
D. (2,-1)
Correct! The parabola is shifted 2 units right and 1 unit down.
In what direction does the parabola -4x = (y + 1)2 open?
A. Up
Incorrect. The y-term is being squared, so the parabola must open either left or right.
B. Down
Incorrect. The y-term is being squared, so the parabola must open either left or right.
C. Left
Correct! The y-term is being squared and "a" is negative, so the parabola opens left.
D. Right
Incorrect. While the y-term is being squared, the "a" is -
1
4
, so the parabola opens left.
For the parabola y − 10 = 1 4 (x+6)2, if the 1 4 is changed to 1 8 , the parabola would —
A. appear to become more narrow
Incorrect. Since the a-value decreased, the parabola would appear to get wider.
B. appear to become wider
Correct! Since the a-value decreased, the parabola would appear to get wider.
C. shift up
Incorrect. Changing the coefficient of the squared term will not shift the graph.
D. shift down
Incorrect. Changing the coefficient of the squared term will not shift the graph.
Given the equations x = (y−2)2 and y = (x−2)2, which of the following are true statements?
I. Both parabolas have the same vertex.
II. Both graphs are shifted 2 units from the origin.
III. The graphs of the two parabolas are reflections of each other over the line y = x.
A. II and III only
Correct! The vertex of the first parabola is (0,2) and the vertex of the second parabola is (2,0), so they don't have the same vertex, but they are both shifted two units from the origin. And since the x and the y variables are switched in the equations, they are inverses of each other and are reflections over the line y = x.
B. I, II, and III
Incorrect. The vertex of the first parabola is (0,2), while the vertex of the second parabola is (2,0), so they don't have the same vertex.
C. II only
Incorrect. II is a true statement, but one of the other statements is also true.
D. I only
Incorrect. I is not a true statement.
What is the equation of the parabola graphed below?
A. y + 4 = -0.5(x + 3)2
B. x + 4 = -0.5(y + 3)2
C. x + 4 = -2(y + 3)2
D. x − 4 = -0.5(y − 3)2
A
Incorrect. Since this parabola opens left, the y-term is being squared, not the x-term.
B
Correct! You interpreted the graph correctly.
C
Incorrect. This parabola is compressed by one half, not stretched by 2.
D
Incorrect. Since the parabola is shifted left 4, the x-term will be replaced with (x −( -4)), or (x + 4) . Likewise, since the parabola is shifted down 3, the y-term will be replaced with (y − (-3)), or (y + 3).