Quadratic Formula and Discriminant Practice

Consider the equation 2x^2 + 8x + k = 0. What is the discriminant in terms of k?

• 64 - 8k

• 16 - 2k

• 64 - 2k

• 16 - 8k

If the solutions of a quadratic equation are 9 and -9, what is the value of b^2 - 4ac?

• 0

• 81

• -81

• 162

Which of the following equations has no real solutions?

• x^2 - 8x - 16 = 0

• -2x^2 + 5x - 6 = 0

• -x^2 + 6x + 1 = 0

• 0

• 1

• 2

• 3

How many non-real solutions do the equations of the following quadratic curves have?

• 0

• 1

• 2

How many x-intercepts does the parabola have if b^2 - 4ac = -5?

• 0

• 1

• 2

• 3

For the graph labeled 'a', determine whether the coefficient 'a' in the quadratic function f(x) = ax^2 + bx + c is greater than 0 or less than 0.

• a > 0

• a < 0

For the graph labeled 'b', determine whether the discriminant b^2 - 4ac is greater than 0, less than 0, or equal to 0.

• b^2 - 4ac > 0

• b^2 - 4ac < 0

• b^2 - 4ac = 0

A cannon is fired from the top of a cliff 26 meters above sea level. The height of the cannonball above sea level, in meters, after t seconds have passed is given by the formula: h = -5t^2 + 56t + 26. If we want to find out when the cannon-ball will reach a height of 200 meters, what equation do we need to solve?

• -5t^2 + 56t + 26 = 200

• -5t^2 + 56t + 26 = 0

• -5t^2 + 56t + 26 = 100

• -5t^2 + 56t + 26 = 56

An object is launched from a height of 90 feet with an initial velocity of 131 feet per second, and after x seconds its height (in feet) is given by h = -16x^2 + 131x + 90. Solve for the number of seconds x after which the object is 20 feet above the ground. Which of the following equations would you solve?

• -16x^2 + 131x + 90 = 20

• -16x^2 + 131x + 90 = 0

• -16x^2 + 131x + 90 = 90

• -16x^2 + 131x + 90 = 131