Question

2. A quadratic function has a vertex at (3,-10) and passes through the point (0,8).
Which of the following equations best represents the function?
F.y = 2(x + 3)^2 + 8
G.y = 2(x + 3)^2 - 10
H. y = (x - 3)^2 - 10
J.y = 2(x - 3)^2 - 10

Answer 1

Given:

Vertex of a quadratic function is at (3,-10).

The quadratic function passes through the point (0,8).

To find:

The equation of the quadratic function.

Solution:

The vertex form of a quadratic function is:

$y=a(x-h)^2+k$              ...(i)

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

Vertex of a quadratic function is at (3,-10). So, $h=3,k=-10$.

$y=a(x-3)^2+(-10)$

$y=a(x-3)^2-10$              ...(ii)

The quadratic function passes through the point (0,8).

Putting $x=0,y=8$ in (ii), we get

$8=a(0-3)^2-10$

$8+10=a(-3)^2$

$18=9a$

Divide both sides by 9.

$2=a$

Putting $a=2$ in (ii), we get

$y=2(x-3)^2-10$

Therefore, the correct option is J.

Answer 2

Answer:

J

Step-by-step explanation: