Question

What is the vertex form of the quadratic function that has a vertex at (2, 1) and goes through the point (3, 2)? O A. y = (x - 2)2 + 1 B. y = 3(x - 2)2 + 1 OC. y = –2(x + 2)2 - 1 OD. y=-3(x - 2)2 + 1

Answer 1

Answer:

Choice D.

Explanation:

The vertex form of a parabola is given by

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

where (h, k) is the vertex.

Now, in our case we have the vertex at (2, 1); therefore, the above gives

$y=a(x-2)^2+1$

Now we just need to find the value of a.

We know that the parabola passes through the point (3, -2), meaning the equation must satisfy x= 3 when y = -2.

Putting in x = 3 and y = -2 in the above equation gives

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

which simplifies to give

$-2=a+1$

subtracting 1 from both sides gives

$a=-3$

Hence, the equation of the quadratic function is

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

which is choice D.