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…

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asked Sep 18, 2020 194k views

2 Answers

Michal Krasny · Answer 1 · 2020-09-22T23:24:04+0000

Answer:

$\large\boxed{y=-3(x-1)^2+4}$

Explanation:

The vertex form of a quadratic function:

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

where (h, k) is a vertex.

We have the vertex (1, 4). Therefore h = 1 and k = 4.

The y-intercept of the function is (0, 1). Put x = 0 and y = 1 to the equation

y=a(x-1)^2+4

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

1=a(-1)^2+4

1=1a+4 subtract 4 from both sides

$-3=a\to a=-3$