y = a(x - h)^{2} + k
is the equation of parabola which is having the vertex (h, k)
The sign of a will decide if there is any reflection or not.
The parabolas shown are the result of translating and/or reflecting the parabola y = x^{2}. Find the equation of each parabola.
Problem 1 :
Solution :
Since the parabola opens down, there is a reflection.
a = -1
Horizontally the graph of y = -x^{2} is not moved.
Vertically the graph of y = -x^{2 }is moved 4 units up.
h = 0 and k = 4
y = -1(x - 0)^{2} + 4
So, the equation from the given graph is
y = -1x^{2} + 4
Problem 2 :
Solution :
Since the parabola opens down, there is no reflection.
a = 1
Horizontally the graph of y = x^{2} is moved 3 units to the left.
Vertically the graph of y = -x^{2 }is not moved.
h = -3 and k = 0
y = 1(x - (-3))^{2 }+ 0
So, the equation from the given graph is
y = (x + 3)^{2}
Problem 3 :
Solution :
Since the parabola opens down, there is reflection.
a = -1
Horizontally the graph of y = -x^{2} is moved 3 units to the right.
Vertically the graph of y = -x^{2 }is moved 3 units up.
h = 3 and k = 3
y = -1(x - 3)^{2 }+ 3
So, the equation from the given graph is
y = -(x - 3)^{2 }+ 3
Problem 4 :
Solution :
Since the parabola opens down, there is no reflection.
a = 1
Horizontally the graph of y = x^{2} is moved 2 units to the right.
Vertically the graph of y = x^{2 }is moved 3 units down.
h = 2 and k = -3
y = 1(x - 2)^{2 }- 3
So, the equation from the given graph is
y = 1(x - 2)^{2 }- 3
Problem 5 :
Solution :
Since the parabola opens down, there is no reflection.
a = 1
Horizontally the graph of y = x^{2} is moved 2 units to the right.
Vertically the graph of y = x^{2 }is moved 1 unit up.
h = 2 and k = 1
y = 1(x - 2)^{2 }+ 1
So, the equation from the given graph is
y = (x - 2)^{2 }+ 1
Problem 6 :
Solution :
Since the parabola opens down, there is no reflection.
a = 1
Horizontally the graph of y = x^{2} is moved 2 units left.
Vertically the graph of y = x^{2 }is moved 1 unit down.
h = -2 and k = -1
y = 1(x - (-2))^{2 }- 1
So, the equation from the given graph is
y = (x + 2)^{2 }- 1
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM