Write the equation for a parabola with a focus at (-3,-5)(−3,−5)left parenthesis, minus, 3, comma, minus, 5, right parenthesis and a directrix at x=-7x=−7x, equals, minus, 7.

(y + 5)² = -16(x + 5)

Step-by-step explanation:

We are told the focus is at (-3, -5)

Directrix is at x = -7

This is a horizontal parabola and thus the general equation is;

(y - k)² = -4p(x - h)

Where;

(h, x) is the coordinate of the vertex.

The axis where the point where the axis of symmetry meets the directrix is at; (-7, -5) since directrix is at x = -7

Thus, coordinates of vertex is;

(-7 + (-3))/2, (-5 + (-5))/2

> (-5, -5)

Thus, equation is;

(y - (-5))² = -4p(x - (-5))

(y + 5)² = -4p(x + 5)

Where p is the distance from vertex to directrix. Thus;

p = -(-7 - (-3))

p = -(-7 + 3)

p = 4

Thus;

(y + 5)² = -4(4)(x + 5)

(y + 5)² = -16(x + 5)

(x+3)(x+7)

step-by-step explanation:

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .