Find the equation, f(x) = a(x-h)2 + k, for a parabola that passes through the point (0, 0) and has (-3, -6) as its vertex. What is the standard form of the equation?

A) The vertex form of the equation is f(x) = −2/3(x + 3)2 - 6. The standard form of the equation is f(x) = 2/3x2 + 4x.

B) The vertex form of the equation is f(x) =2/3(x + 3)2 - 6. The standard form of the equation is f(x) = −2/3x2 - 4x.

C) The vertex form of the equation is f(x) =−2/3(x - 3)2 - 6. The standard form of the equation is f(x) = 2/3x2 - 4x.

D) The vertex form of the equation is f(x) = 2/3(x + 3)2 - 6. The standard form of the equation is f(x) = 2/3x2 + 4x.

The answer is D because the value of a (2/3) is positive, and only D has it positive in both forms.

Step-by-step explanation:

The vertex form of the equation for a parabola is a(x – h)² + k, and the vertex is (h,k).

The standard form of the parabola equation is  ax² + bx + c.

From your given information, the vertex is (-3, -6) so by plugging that into the equation, we get a[x – (-3)]² + (-6) = a(x + 3)² - 6

so f(x) = a(x +3)² - 6 and we put in the point (0,0) we get

0 = a(0 +3)² - 6 and solve for a.

0 = a(3)² - 6

 0 = 9a -6  (add 6 to both sides to get a by itself)

+6         +6

6   = 9a  (divide both sides by 9 to get a by itself)

9      9

6/9 = a  (we simplify 6/9 by reducing both numbers by 3 to get 2/3)

a = 2/3  therefore our vertex form is now f(x) = (2/3)(x +3)² - 6.

We have to expand our equation to find the standard form.

(x +3)² = (x+3)(x+3) = x² + 3x + 3x +9 = x² +6x+ 9 (plug it back in)

(2/3)(x² +6x+ 9) - 6

2/3x² + (2/3)6x+ (2/3)9  - 6

2/3x² +4x+ 6   - 6

f(x) = 2/3x² + 4x is standard form; vertex form is now f(x) = (2/3)(x +3)² - 6

answer:   segregation violated the equal protection clause of the 14th amendment, which holds that no state can “deny to any person within its jurisdiction the equal protection of the laws.”

details/explanation:

brown v. board of education of topeka, decided by the us supreme court in 1954, ruled that all americans are entitled to the same civil liberties and protections in regard to access to education. until that decision, it was legal to segregate schools according to race, so that black students could not attend the same schools as white students.   an older supreme court decision, plessy v. ferguson (1896), had said that separate, segregated public facilities were acceptable as long as the facilities offered were equal in quality.   in the case of brown v. board of education, that standard was challenged and defeated.   segregation was shown to create inequality, and the supreme court unanimously ruled segregation to be unconstitutional.

the ruling was important in advancing civil rights because it affirmed that the 14th amendment applies to all rights and privileges of citizens, including access to   education.   this was being violated by states whose laws supported the segregation of schools.   section 1 of the 14th amendment reads as follows: