What is the purpose of using the quadratic formula?
To solve for the unknown variable in a quadratic equation. To find the x-intercepts (roots).
100
The formula to find the x-coordinate of the vertex
What is -b/(2a)
100
Simplify (x + 4)(2x + 5)
What is 2x^2 + 13x + 20
200
Identify the real and imaginary part of -4i + 7
What is: the real part is 7, the imaginary part is -4
200
The minimal distance d (in ft) it takes for a certain car to stop is approximated by the formula d = 0.042s^2 + 1.1s + 4, where s is the speed (in mph). If a car took 200' to stop, how fast was it traveling?
About 56 mph
200
The equation of vertex form of a parabola
What is y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola and a represents the leading coefficient of the quadratic form.
200
Solve abs(x - 6) = 15.6
What is x=21.6 or x=-9.6
300
V = ZI relates voltage (v) to current (I) and impedance (Z). Find the voltage if the current is 11 + 7i amps and the impedance is 7-3i ohms.
What is 95 + 9i volts
300
The solution to x^2 + 2x - 15 = 0
What is = -5 or x = 3
300
y = 4x^2 has been translated 3 units left and 2 units down. Write the equation of its image in vertex form. What is the vertex of this image?
What is y = 4(x + 3)^2 - 2. The vertex is (-3, -2)
300
What is the domain of the absolute value function?
What is all real numbers
400
V = ZI relates voltage (v) to current (I) and impedance (Z). Find the impedance if the voltage is 852 + 216i ohms and the current is 30-12i volts.
What is 22 + 16i
400
The number of solutions to 15x^2 - 3x + 7 = 0.
What is 0 real solutions b/c the discriminant is negative.
400
Write y - 3 = 1/4(x - 2)^2 in standard form
What is y = 1/4x^2 - x + 4
400
Why is the range of the absolute value function and the quadratic function the same, y is greater than or equal to 0?
Because the outputs of each function represent positive values; either distance from zero or squaring.
500
Simplify (2 + i) / (3 - i)
What is 1/2 + 1/2i
500
Give the number of intercepts of:
y + 14 = -3(x - 2)^2
0 - these two lines do not cross
500
Write in vertex form by completing the square.
y = x^2 - 6x + 10
What is y = (x - 3)^2 + 1
500
A square an a circle have the same area. The square has side 6 inches. What is the diameter of the circle?