Question

The directrix and vertex of a parabola are shown on the graph. What is the vertex form of the equation for the associated parabola?

Answer 1

Considering the directrix and vertex given in the graph, the equation of the parabola is:

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

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 - k)² = 4p(x - h).

In which the directrix is the line x = h - p.

Looking at the graph, we have that:

• The vertex is (-2,-2), hence h = k = -2.

• The directrix is x = -1, hence -1 = -2 - p -> p = -1.

Thus the equation is:

(y + 2)² = -4(x + 2).

Writing x as a function of y:

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

More can be learned about the equation of a parabola at brainly.com/question/17987697

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