Quadratic Formula
x2 + 4x - 12 = 0
x = 2 and x = -6
x2 + 8 = 28
x = 2√5 and x = -2√5
What is the discriminant of
-2x2 - x - 1 = 0
-7
The solutions to quadratic equations represent
2x2 + 9x + 4 = -3
x = -7/2
x = -1
9x2 - 23 = 0
√23/3 and -√23/3
Find the discriminant and then state the number of real or imaginary solutions.
9m2 + 6m + 6 = 5
The discriminant is 0 meaning 1 real solution
Given the equation -5x2 + 5 = -10x, identify a, b and c
a = -5, b = 10, and c = 5
x2 - 3x - 15 = 0
x = (3 + √69) / 2
x = (3 - √69) / 2
-5x2 = 500
No real solution
Find the discriminant and then state the number of real or imaginary solutions.
-4r2 - 4r = 6
The discriminant is -80 meaning no real solution (or 2 imaginary solutions)
True or False: The following equation can be solved by square roots.
3x2 + 5x = 49
False
25x2 + 9 = 30x
x = 3/5
4(x+8)2 = 144
x = -14 and x = -2
Find the discriminant and then state the number of real or imaginary solutions.
-7x2 + 8x = 0
The discriminant is 64 meaning there are 2 real solutions
True or False: A quadratic equation with no real solution never crosses the y-axis
False
x2 - 6x = 15
x = 3 + 2√6
x = 3 - 2√6
-2(x-5)2 + 6 = -40
x = 5 + √23
x = 5 - √23
Find the discriminant and then state the number of real or imaginary solutions.
-x2 - 9 = 6x
The discriminant is 0 meaning 1 real solution.
A batter hits a pitched baseball when it is 3 feet off the ground. After it is hit, the height h (in feet) of the ball at time t (in seconds) is modeled by h = -16t2 + 80t +3 where t is the time in seconds. Find the time when the ball hits the ground rounded to the nearest hundredth place.
t = 5.04 seconds