1Which quadratic functions are shown when \( y = x^2 \) and \( y = (x - 2)^2 \) are drawn on one graph?
2Are the graphs of \( y = x^2 \) and \( y = (x - 2)^2 \) the same as each other?
3What are the coordinates of the vertices of \( y = x^2 \) and \( y = (x - 2)^2 \)?
4How many units to the right of the vertex of \( y = x^2 \) is the vertex of \( y = (x - 2)^2 \)?
5Do the other corresponding points of \( y = x^2 \) and \( y = (x - 2)^2 \) show the same relation as the vertices?
6What quadratic function do we get when \( y = x^2 \) is moved 2 units to the left, and what does its graph look like?
7When five points of \( y = x^2 \) are each moved 2 units up and joined, what size and shape does the new curve have?
8Write the function of the curve formed by moving every point of \( y = x^2 \) 2 units up.
9Choose the correct option. The coordinates of the turning point of the graph of \( y = ax^2 \) are: (0, 0), (k, 0), (h, k) or (h, 0)?
10Choose the correct option. The shape of \( y = -ax^2 \), where \( a > 0 \), is: \( \cup \), \( \cap \), \( \subset \) or \( \supset \)?
11Choose the correct option. The parabola given by \( y = 2x^2 \) is symmetric about: the X-axis, the Y-axis, the line \( y = 0 \) or the line \( y = 1 \)?
12Choose the correct option. The vertex of \( y = a(x - h)^2 + k \) is: (0, 0), (k, 0), (h, k) or (h, 0)?
13Choose the correct option. The vertex of the parabola \( y = x^2 - 2x + 1 \) is: (0, 0), (-1, 0), (1, 0) or (1, 1)?
14Write \( y = x^2 \) in vertex form and describe how to sketch it.
15Write \( y = 2x^2 \) in vertex form and describe its graph.
16Write \( y = -3x^2 \) in vertex form and describe its graph.
17Write \( y = x^2 + 2 \) in vertex form and describe its graph.
18Write \( y = x^2 - 5 \) in vertex form and describe its graph.
19Write \( y = (x - 3)^2 \) in vertex form and describe its graph.
20Write \( y = (x + 3)^2 \) in vertex form and describe its graph.
21Write \( y = x^2 + 2x + 1 \) in vertex form and describe its graph.
22Write \( y = x^2 - 4x + 3 \) in vertex form and describe its graph.
23Write \( y = -x^2 - 3x + 2 \) in vertex form and describe its graph.
24Write \( y = x^2 - x - 2 \) in vertex form and describe its graph.
25Write \( y = -x^2 + 7x + 12 \) in vertex form and describe its graph.
26For \( x^2 - 4x + 7 = 0 \), write \( y = x^2 - 4x + 7 \) in vertex form, find the vertex and the axis of symmetry, and describe the graph as a transformation of \( y = x^2 \).
27For \( x^2 - 6x + 13 = 0 \), write \( y = x^2 - 6x + 13 \) in vertex form, find the vertex and the axis of symmetry, and describe the graph as a transformation of \( y = x^2 \).
28For \( x^2 - 8x + 21 = 0 \), write \( y = x^2 - 8x + 21 \) in vertex form, find the vertex and the axis of symmetry, and describe the graph as a transformation of \( y = x^2 \).
29For \( x^2 + 2x - 4 = 0 \), write \( y = x^2 + 2x - 4 \) in vertex form, find the vertex and the axis of symmetry, and describe the graph as a transformation of \( y = x^2 \).
30For \( x^2 + 2x + 1 = 0 \), write \( y = x^2 + 2x + 1 \) in vertex form, find the vertex and the axis of symmetry, and describe the graph as a transformation of \( y = x^2 \).
31Why does \( y = (x - 5)^2 \) lie to the right of \( y = x^2 \) even though the number 5 is subtracted?
32The graph of \( y = x^2 \) is moved 4 units left and then 2 units down. Write the new function, its vertex and its axis of symmetry.
33Does a vertical transformation change the axis of symmetry of \( y = x^2 \)? Explain.