Question

Write the equation of the parabola in vertex form. vertex (4,4), point (3, -1)

Answer 1

Answer:

$y=-5(x-4)^2+4$

Step-by-step explanation:

Equation of the Quadratic Function

The vertex form of the quadratic function has the following equation:

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

Where (h, k) is the vertex of the parabola, and a is a coefficient different from zero.

The vertex is located at (4,4).

Substituting the coordinates of the vertex, the equation of the function is:

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

The value of a will be determined by using the given point (3,-1).

$-1=a(3-4)^2+4$

Operating:

$-1=a(1)+4$

Solving:

$a=-5$

The equation of the graph is:

$\boxed{y=-5(x-4)^2+4}$