Parabolic Equations

Which of the following is true about quadratic functions?

• The standard form of a quadratic function is... "y = ax² + bx + c".

• The second differences of the y-values are constant.

• The graph of a quadratic is parabolic.

• All of the above

Which of the following equations matches the table shown?

• y = 6.2x² + 300

• y = -6.2x² + 300

• y = -6.2x² - 300

• y = 6.2x² - 300

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

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

• vertex

• focus

• parabola

Lava coming from the eruption of a volcano follows a parabolic path.  The height h in feet of a piece of lava t seconds after it is ejected from the volcano is given by h(t) = -t² + 16t + 936.  After about how many seconds does the lava reach its maximum height?

• 12

• 20

• 8

• 5

Compare ƒ(x) = -2x² - 8x + 20 to the graph of g(x) shown.  What can you conclude about the two functions?

•  ƒ(x) has a greater maximum than g(x).

• g(x) has a greater maximum than ƒ(x).

• ƒ(x) has a minimum, while g(x) has a maximum.

• g(x) and ƒ(x) have the same maximum.

How many solutions does this system of equations have?

Solve the system above.

• (1,5)

• (5,-2)

• (-2,5)

• (5,1)

A parabola that opens up has a focus point at (2, 5) and a directrix at y = -1.  Write the equation of this parabola.