The vertex of a quadratic function is located at (1, 4), and the y-intercept of the function is (0, 1). what is the value of a if the function is written in the form y = a(x – h)2 + k?

y = a(x – h)² + k
So the vertex is (1, 4). this is (h, k)

y = a(x – 1)² + 4
now we solve for k by using the point it gives us and plugging 0 in for x and 1 in for y and solving

1 = a(0 – 1)² + 4      simplify
1 = a( -1)² + 4          square the -1
1 = a(1) + 4              no need for that 1 anymore
1 = a + 4                subtract 4 from each side
-3 = a