Question

A quadratic function has a vertex at (3,4). This quadratic also goes through the point (7, 12). Find the a value A using the information.

Answer 1

a = 1/2

Step-by-step explanation:

In the equation of the form

y = a(x - h)² + k

The vertex is (h, k). So, we can replace (h, k) with (3, 4) as follows

y = a(x - 3)² + 4

Now, we can use the point (7, 12) to find the value of a, replacing (x, y) = (7, 12) and solving for a, so

12 = a(7 - 3)² + 4

12 = a(4)² + 4

12 = a(16) + 4

12 - 4 = a(16)

8 = a(16)

8/16 = a

1/2 = a

Therefore, the value of a is 1/2.