Question

T he equation for a parabola with directrix y = –p and focus (0, p) is:
https://media.glynlyon.com/g_alg02_ccss_2013/8/equation_parabola.gif

What is the vertex?

(0, p)

(0, -p)

(0, 0)

(p, 0)

(-p, 0)

Answer 1

The vertex is equidistant from the directrix and the focus, so it would be at the origin.

Answer 2

(0,p)?

Answer 3

No, the origin is (0,0)

Answer 4

ohhhh ok, thank you

Answer 5

yw

Answer 6

can you help me with another question?

Answer 7

A parabola can be translated so does not have to have its vertex at the origin or on an axis. (Remember that a translation moves or maps every point the same distance and direction.)

The equation for a parabola with directrix y = k – p and focus (h, k + p) is: https://media.glynlyon.com/g_alg02_ccss_2013/8/equation_parabola_directrix.gif

The value of k changes the placement of the parabola. Assume that p > 0. There are 3 cases to consider:

k > 0
k = 0
k < 0

Describe the location of the vertex of the parabola relative to the x-axis. How many zeros does the polynomial have?

Answer 8

If \(k>0\), then the vertex lies above the x-axis, so there are no real roots/zeros.

If \(k=0\), then the vertex lies on the axis, so there's one zero.

If \(k<0\), then the vertex lies below the axis, so there are two zeros.

Answer 9

Thank you for the help.