Question

Select the quadratic function that corresponds to each graph below

Answer 1

Answer:

1.  $y=(x+3)^2-4$

2. $y=(x+4)^2-3$

3. $y=(x-3)^2+4$

4. $y=(x-4)^2+3$

Step-by-step explanation:

The vertex from of a quadratic function is

$y=a(x-h)^2+k$

where, a is constant and (h,k) is vertex.

(1)

The vertex of the parabola is (-3,-4).

$y=a(x-(-3))^2+(-4)$

$y=a(x+3)^2-4$

The graph is passes through the point (-1,0).

$0=a(-1+3)^2-4$

$4=4a$

$1=a$

$y=(1)(x+3)^2-4$

$y=(x+3)^2-4$

Therefore, the required equation is $y=(x+3)^2-4$.

Similarly,

(2)

The vertex of the parabola is (-4,-3).

$y=a(x+4)^2-3$

The graph is passes through the point (-3,-2).

$-2=a(-3+4)^2-3$

$a=1$

Therefore, the required equation is $y=(x+4)^2-3$.

(3)

The vertex of the parabola is (3,4).

$y=a(x-3)^2+4$

The graph is passes through the point (2,5).

$5=a(2-3)^2+4$

$a=1$

Therefore, the required equation is $y=(x-3)^2+4$.

(4)

The vertex of the parabola is (4,3).

$y=a(x-4)^2+3$

The graph is passes through the point (3,4).

$4=a(3-4)^2+3$

$a=1$

Therefore, the required equation is $y=(x-4)^2+3$.

Answer 2

C B A are the orders of the answers