Question

Write the relation for a parabola that satisfies each condition:
The graph of y=x^2 is stretched vertically by a factor of 3/2, then translated left 4 units.

Answer 1

Graph of Y = x^2.

(X , Y)

(-2 , 4)

(-1 , 1)

V(0 , 0)

(1 , 1)

(2 , 4).


Add -4 to each value of X. Add 3/2(1.5)
to each Y value:

(X , Y)

(-6 , 5.5)

(-5 , 2.5)

V(-4 , 1.5)

(-3 , 2.5)

(-2 , 5.5)

Graph the two parabolas on the same graph for better comparison.


V(-4 , 1.5), P(-3 , 2.5).

Y = a(x - h)^2 + k.

2.5 = a(-2 + 4)^2 + 1.5,
2.5 = a + 1.5,
-a = 1.5 - 2.5,
-a = -1,
a = 1.

Eq2: Y = (X + 4)^2 + 1.5.