Question

1. Answer the following questions about y = 4(x-3)2 +1 compared to the parent function y = x²

a) Does the graph open up or down?
b) Does this graph have a maximum or a minimum?
c) What is the coordinate point of the vertex?
d) What is the equation of the axis of symmetry?
e) Is the graph narrower or wider or the same as the parent function?
f) Does the graph shift left or right?
g) Does the graph shift up or down?
By how many units?
By how many units?
2. Answer the following questions about y=-0.5(x + 5)² -4 compared to the parent function y = x²
a) Does the graph open up or down?
b) Does this graph have a maximum or a minimum?
c) What is the coordinate point of the vertex?
d) What is the equation of the axis of symmetry?
e) Is the graph narrower or wider or the same as the parent function?
f) Does the graph shift left or right?
g) Does the graph shift up or down?
By how many units?
By how many units?
3. See if you can write equations, in
form, that fit the following properties:
a. This equation is not stretched or shrunk and opens up. It is also shifted left 7 units and up 4 units.
b. This equation is narrower by a factor of 2, opens down, shifted right 3 units, and shifted down 9 units.

Answer 1

1.
`\( y = 4(x-3)^2 + 1 \)`: (a) up, (b) min, (c) (3,1), (d) x = 3 , (e) narrower by 4, (f) right 3, (g) up 1.

2.
`\( y = -0.5(x + 5)^2 - 4 \)` : (a) down, (b) max, (c) (-5,-4), (d) x = -5 , (e) narrower by 0.5, (f) left 5, (g) down 4.

3. a.
`\( y = x^2 + 4 \):` opens up, left 7, up 4.

b.
`\( y = -2(x - 3)^2 - 9 \)`: narrows by 2, opens down, right 3, down 9.

1. For the function
`\( y = 4(x-3)^2 + 1 \)` compared to the parent function
`\( y = x^2 \):`

a) The graph opens up as the coefficient of the squared term (4) is positive.

b) The graph has a minimum since the parabola opens upward.

c) The coordinate point of the vertex is (3, 1).

d) The equation of the axis of symmetry is x = 3.

e) The graph is narrower than the parent function due to the vertical stretch by a factor of 4.

f) The graph shifts right by 3 units (opposite to the sign inside the parentheses).

g) The graph shifts up by 1 unit.

2. For the function
`\( y = -0.5(x + 5)^2 - 4 \)` compared to the parent function
`\( y = x^2 \):`

a) The graph opens down as the coefficient of the squared term (-0.5) is negative.

b) The graph has a maximum since the parabola opens downward.

c) The coordinate point of the vertex is (-5, -4).

d) The equation of the axis of symmetry is x = -5.

e) The graph is narrower than the parent function due to the vertical compression by a factor of 0.5.

f) The graph shifts left by 5 units (opposite to the sign inside the parentheses).

g) The graph shifts down by 4 units.

3. Equations that fit the given properties:

a.
`\( y = x^2 \)` shifted left 7 units and up 4 units:
`\( y = (x + 7)^2 + 4 \).`

b.
`\( y = -2(x - 3)^2 - 9 \)` (This equation combines a vertical stretch by 2, a right shift by 3 units, and a downward shift by 9 units, while maintaining an opening upward orientation).