Algebra Jeopardy: Quadratics

Vocab

100

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Parabola

200

Standard form of a quadratic equation

 y = ax² + bx + c

300

What does the following equation give us? x = -b/2a

Axis of Symmetry

400

What is the formula used to find the x-coordinate of the vertex?

x = -b / 2a

500

After finding the x-coordinate, how do you find the y-coordinate?

Plug x back into the original equation

Graph

100

If the "a" value is negative, does the graph open up or down?

Down

200

The highest or lowest point on a parabola; the "turning point."

Vertex

300

What is the imaginary vertical line that passes through the vertex?

Axis of Symmetry

400

Does the function $y = -2x^2 + 8x - 3 have a Maximum or a Minimum point?

Maximum (because a is negative)

500

Quality of a prabola determined by the value of  |a|

Width

Axis of Symmetry & Vertex

100

True or False: The Axis of Symmetry is always a horizontal line.

False (It is always a vertical line)

200

Find the x-coordinate of the vertex for: $y = 2x^2 - 8x + 5$.

x = 2

300

What is the equation for the Axis of Symmetry for y=x² - 6x + 8?

x=3

400

Find the vertex (x,y) for: y = x² + 6x + 5

(-3, -4)

500

If the Axis of Symmetry is x = -5, and the graph passes through (-5, 10), what is the Vertex?

(-5, 10)

Solving Quadratics

100

What do we call the points where the graph touches or crosses the x-axis?

x-intercepts (Roots/Zeros)

200

How many x-intercepts does a parabola have if it opens UP and the vertex is at (2, 4)?

Zero (it never reaches the x-axis)

300

Solve for the zeros by setting y = 0: y = x² - 16

x = 4 and x = -4

400

Divide by 5, then solve for the zeros: y = 5x² - 125

x=5 and x=-5

500

Why does the equation y = x² + 25 have no real zeros?

Because you can't take the square root of a negative number (-25)

Domain & Range

100

For a standard quadratic function, the Domain is always what?

All Real Numbers

200

Which coordinate of the vertex (x or y) do you use for the Range?

The y-coordinate

300

If a parabola opens UP and the vertex is (2, 5), what is the Range?

y>5

400

If a parabola opens DOWN and the vertex is (-1, 10), what is the Range?

y<10

500

Does "Domain" refer to the horizontal (x) or vertical (y) spread?

Horizontal (x) spread