Question

What is the equation of a parabola if the vertex is (1, 4) and the directrix is located at y = 7?

Answer 1

According to the vertex and the directrix of the given parabola, the equation is:

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

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

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

In which a is the leading coefficient.

The directrix is at y = k + 4a.

In this problem, the vertex is (1,4), hence:

$h = 1, k = 4$

The directrix is at y = 7, hence:

$4 + 4a = 7$

$a = \frac{3}{4}$

Hence, the equation is:

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

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

More can be learned about the equation of a parabola at brainly.com/question/26144898