Jeopardy: Solving Quads

Discriminant &Solve by Graphing

100

When the value of the discriminant is negative, there are this many solutions.

Zero or No Solutions

200

What is the value of the discriminant in the equation:

y = 3x² + 10x + 2

76

300

A parabola has a vertex of (3, -2) and opens up. Determine how many x-intercepts the graph has.

2 Solutions

400

A parabola has a vertex of (-5, 0) and opens up. How many x-intercepts would the graph have?

1

500

Molly graphs a parabola with x-intercepts of (3, 0) and (7, 0). What do you know about the value of the discriminant?

It must be positive.

Solve by Factoring

100

Solve the quadratic equation by factoring:

y = x² + 3x - 28

{-7, 4}

200

Solve the quadratic equation by factoring:

3x² + 8x = -4

{-2/3, -2}

300

Solve the quadratic equation by factoring:

4x² = 25

{5/2, -5/2}

400

Solve the quadratic equation by factoring:

x² + 14x = 0

{0, -14}

500

Solve the quadratic equation by factoring:

6x² + 12x - 7 = -2x² + 2x

{-7/4, 1/2}

Solve by Square Roots or QF

100

Solve using the square root method:

2x² - 50 = 0 

{5, -5}

200

Solve using the Square Root Method:

(x+5)² - 36 = 0

{1, -11}

300

Solve using the square root method:

-3(x+7)² = -48

{-3, -11}

400

Solve using the square root method:

5x² - 40 = 0

{2rad2, -2rad2}

500

Solve using the Quadratic Formula:

2x² - 3x - 15 = 5

{4, -5/2}

Converting Equations

100

If you want to know the x-intercepts of a quadratic equation, which form do you want the equation in?

Factored Form

200

Rewrite the equation in vertex form:

y = -x² - 6x - 5

y = -(x+3)² + 4

300

Rewrite the equation in Standard Form:

y = -2(x+1)(x-5)

y = -2x² + 8x + 10

400

Which form of a quadratic equation is most helpful when you want to know the y-intercept?

Standard Form

500

Rewrite the equation in Factored Form:

y = (x - 4)² - 36

y = (x - 10)(x + 2)

Word Problems

100

Mark kicks a soccer ball. The equation: y = 2x² + 10x represents the height of the ball (in feet) after "x" seconds. Mark finds that the two x-intercepts/solutions are 0 and 5. What information does that give you about the soccer ball?

The ball is in the air for 5 seconds.

200

Mark kicks a soccer ball. The equation: y = 2x² + 10x represents the height of the ball (in feet) after "x" seconds. Mark finds that the vertex of the parabola is (2.5, 37.5) What does this tell you about the soccer ball?

The ball reaches its maximum height of 37.5 feet after 2.5 seconds in the air.

300

Sasha throws a penny off her balcony. The equation

y = -3x² + 7x + 54 represents the height of the penny in feet after "x" seconds. What does the 54 represent in the context?

The 54 is the y-intercept, the initial height. So the balcony is 54 feet from the ground.

400

Shai throws a football to her friend. The equation:

y = -16x² + 48x represents the height of the ball in feet after "x" seconds. What is the maximum height that the ball reaches?

36 feet

500

Shai throws a football to her friend. The equation:

y = -16x² + 48x represents the height of the ball in feet after "x" seconds. After how many seconds will her friend catch the ball?

3 seconds