Part C
1 answer:
a = 1, b =14 and y-coordinate is 6 when x = 0.
Solution:
Let us first write the equation of a line.
Take the points are (2, 2) and (6, 10).
Slope of the line:
m = 2
Point-slope formula:
y - 10 = 2(x - 2)
y - 10 = 2x - 4
Add 10 on both sides,we get
y = 2x + 6
Equation of a line is y = 2x + 6.
To find (a, 8), substitute x = a and y = 8 in the equation,
8 = 2a + 6
Subtract 6 from both sides, we get
2 = 2a
a = 1
To find (4, b), substitute x = 4 and y = b in the equation,
b = 2(4) + 6
b = 8 + 6
b = 14
Substitute x = o in the equation.
y = 2(0) + 6
y = 6
The y-coordinate is 6 when x = 0.
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Answer:
The graph of parent function reflected across x-axis, vertically stretched by factor 2 and shift 5 units left 3 units down.
Step-by-step explanation:
The parent function is
The given function is
If an expression is , then we have to add
in it to make it perfect square.
In the parenthesis the value of b is 10.
Add and subtract 25 in the parenthesis.
.... (1)
The translation is defined as
.... (2)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<|k|<1, then the graph compressed vertically by factor k and if |k|>1, then the graph stretch vertically by factor k.
Negative k represents the reflection across x-axis.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
From (1) and (2) it is clear that k=-2, a=5 and b=-3.
It means graph of parent function reflected across x-axis, vertically stretched by factor 2 and shift 5 units left, 3 units down.
