Question

40 POINTS TO WHO EVER CAN ANSWER THIS!!!!!








Which quadratic function does the graph represent? The vertex is at (-2,-3) and the point is at (0,7)


A.)f(x)=5/2(x+2)^2-3

B.) f(x)= 10/9(x+2)^2-3

C.) f(x)=7(x-2)^2-3

D.)f(x)=5(x-2)^2-3

Answer 1

Answer:

y = 2.5(x + 2)^2 - 3

The answer is A

Step-by-step explanation:

The general equation for the vertex is

y  =  a (x + b)^2 + c

a we are not certain about

b = 2

c = - 3

y = a(x + 2)^2 - 3 Now we have to solve for a.

a is found by using the one point we know (0,7) It means when x = 0 y = 7 so just put those two numbers in.

7 = a(0 - 2)^2 - 3

7 = a (- 2)^2 - 3       Add 3 to both sides.

7 + 3 = a(4)              Combine 7 and 3

10 = 4a                     Divide by 4

10/4 = a                    Do the actual division    

2.5 = a

Answer: See above

Answer 2

A

the equation of a parabola in vertex form is

y = a(x - h )² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here the vertex = (- 2, - 3 ), thus

y = a(x + 2 )² - 3

to find a substitute (0, 7 ) into the equation

7 = 4a - 3 ( add 3 to both sides )

10 = 4a ( divide both sides by 4 )

a = $\frac{10}{4}$ = $\frac{5}{2}$

y = $\frac{5}{2}$(x + 2 )² - 3