Parabola Conic Section

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

• (5, -4)

• (-5, -4)

• (-15, -4)

• (15, -4)

Use the information provided to write the general equation of the parabola with focus at (5, 2) and directrix x = -3.

A cross-section of a design for a travel-sized solar fire starter is shown in the Figure above. The sun’s rays reflect off the parabolic mirror toward an object attached to the igniter. Because the igniter is located at the focus of the parabola, the reflected rays cause the object to burn in just seconds. Find the equation of the parabola that models the fire starter. Assume that the vertex of the parabolic mirror is the origin of the coordinate plane.

The figure above shows a diagram for the main section of a suspension bridge. The shape of the curved cable can be closely approximated by a parabola. As shown in the figure, there are 17 vertical support wires. These, along with the two 10.6-m end posts, are equally spaced at 5-m intervals. At the center of the bridge, the vertical support wire (from the vertex of the parabola to the roadway) has a length of 0.6 m.
In the figure, let the road correspond to the x-axis in an x-y coordinate system, with the vertex of the parabolic cable located at (0, 0.6). Find an equation in standard form of the parabola.

Given a parabola with a vertex at (4,3) and a directrix of y=1, write the equation of the parabola.

Mathematical Equivalence

ON

In the equation of a parabola, d is the distance from the ​ (a)   to the ​ (b)   .

• vertex

• focus

• parabola

In a horizontal parabola, which coordinate changes from the vertex to the focus?

Mathematical Equivalence

ON

In a vertical parabola, which coordinate changes from the vertex to the focus?

Mathematical Equivalence

ON

Given a parabola with a vertex of (4,0) and a focus of (4,-1) write the equation of the parabola.

Mathematical Equivalence

ON

In a parabola, "p" tells you the distance from the ​ (a)   to the ​ (b)   and ​ (c)  

• vertex

• focus

• directrix

• origin

• parabola

• axis