Precalculus Practice Test 9.19.3 - South Minneapolis High School printable pdf download

Precalculus Practice Test 9.19.3 - South Minneapolis High School

Precalculus Practice Test 9.1‐9.3

Name: __________________________ Date: _____________

1. Find the standard form of the parabola with the given characteristic and vertex at the

origin.

directrix: x = –4

The directrix

x = –4

is a vertical line, 4 units from the origin.

Because we have been given that the vertex of the parabola is the origin and we know that p is

the distance from the vertex to the directrix (p is also the distance from the vertex to the focus),

we can conclude that p is equal to 4.

Since the directrix is a vertical line 4 units to the left of the origin, we can conclude that the

parabola will open to the right.









y  k

 4 p x  h

The equation will take the form

The vertex is the origin, so h and k are both zero. p is 4. Thus, the equation is





 





y  0

 4 4

x  0

 16x

2. Find the equation of the graph.

This parabola opens upward. This means that it takes the

(x  h)

 4 p(y  k)

form

. However, we can clearly see

 4 py

that the vertex is the origin, so

. We can see

that the point (1,4) lies on the graph, so we can plug this

into the equation and solve for the constant.

 4 p(4)

(1)

 4 p

Notice that we can just solve for 4p instead of p. The



equation of the parabola is

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Precalculus Practice Test 9.19.3 - South Minneapolis High School

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