Answer:
2a) -2
b) 8
Step-by-step explanation:
<u>Equation of a parabola in vertex form</u>
f(x) = a(x - h)² + k
where (h, k) is the vertex and the axis of symmetry is x = h
2 a)
Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):
f(x) = a(x - 2)² - 6
If one of the x-axis intercepts is 6, then
f(6) = 0
⇒ a(6 - 2)² - 6 = 0
⇒ 16a - 6 = 0
⇒ 16a = 6
⇒ a = 6/16 = 3/8
So f(x) = 3/8(x - 2)² - 6
To find the other intercept, set f(x) = 0 and solve for x:
f(x) = 0
⇒ 3/8(x - 2)² - 6 = 0
⇒ 3/8(x - 2)² = 6
⇒ (x - 2)² = 16
⇒ x - 2 = ±4
⇒ x = 6, -2
Therefore, the other x-axis intercept is -2
b)
Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):
f(x) = a(x - 2)² - 6
If one of the x-axis intercepts is -4, then
f(-4) = 0
⇒ a(-4 - 2)² - 6 = 0
⇒ 36a - 6 = 0
⇒ 36a = 6
⇒ a = 6/36 = 1/6
So f(x) = 1/6(x - 2)² - 6
To find the other intercept, set f(x) = 0 and solve for x:
f(x) = 0
⇒ 1/6(x - 2)² - 6 = 0
⇒ 1/6(x - 2)² = 6
⇒ (x - 2)² = 36
⇒ x - 2 = ±6
⇒ x = 8, -4
Therefore, the other x-axis intercept is 8
5(2x^2 - 5x - 3) = 5(2x + 1)(x - 3)
hope this helps :)
Answer:
(x, y)→(x − 8, y − 7)
Step-by-step explanation:
If we take the hexagon DEFGHI coordinates and apply the rule (x, y)→(x − 8, y − 7) we get:
D (2, 5) → (2 - 8, 5 - 7) = (-6, -2) which corresponds to point D'
E (5, 5) → (5 - 8, 5 - 7) = (-3, -2) which corresponds to point E'
F (6, 3) → (6 - 8, 3 - 7) = (-2, -4) which corresponds to point F'
G (5, 1) → (5 - 8, 1 - 7) = (-3, -6) which corresponds to point G'
H (2, 1) → (2 - 8, 1 - 7) = (-6, -6) which corresponds to point H'
I (1, 3) → (1 - 8, 3 - 7) = (-7, -4) which corresponds to point I'
