Answer:
Step-by-step explanation:
To understand the transformation better we will take a point B first.
Coordinates of B → (3, 0)
When we rotate this point by 180° counterclockwise about the origin, rule to be followed,
(x, y) → (-x, -y)
By this rule, coordinates of B'' will be,
B(3, 0) → B''(-3, 0)
Now we translate the point B by 2 units right.
Rule for the translation is,
(x, y) → [(x + 2), 0]
Following this rule,
B''(-3, 0) → B'[(-3+2), 0]
→ B'(-1, 0)
We can conclude with the statement, "Figure ABCD was rotated by 180° about the origin followed by the translation of 2 units to the right" to get the new figure A'B'C'D' similar to pre-image ABCD.
Answer:
6(2n-3)
Step-by-step explanation:
Factor out 6 from the expression
Answer:
a. y = 3 × (x + 2)(x - 8)
b. y = 3·(x - 3)² - 75
c) y = 3·x² - 18·x - 48
Step-by-step explanation:
The x-intercept of the quadratic equation are (-2, 0), (8, 0)
The stretch of the quadratic equation = 3
We have;
a. The factored form y = 3 × (x + 2)(x - 8)
b. From the vertex form, we have;
y = 3 × (x + 2)(x - 8) = 3·x² - 18·x - 48
y = 3·x² - 18·x - 48
The vertex form a(x - h)² + k
Where;
h = -b/(2·a) = 18/6 = 3
h = 3
k = c - b²/(4·a) = -48 - (18²)/12 = -75
The vertex form 3·(x - 3)² - 75
c) The standard form of the quadratic equation, y = a·x² + b·x + c
The standard form of the quadratic equation is y = 3·x² - 18·x - 48.