Terms/Formulas
a + bi
Complex Number
What is the discriminant?
b2 - 4ac
Do the squaring (3x - 9)2
9x2 - 54x + 81
What is the complex conjugate of 8 + 2i
8 - 2i
f(x) = 3x2 + 2x - 11
find f(-4)
29
i2 = ?
-1
What is the general equation of a quadradic function?
y = ax2 + bx+ c
Find the y- intercept of y - 1 = x2 + 8x + 20
(0, 21)
Simplify the square root of -25
5i
f(x) = 3x2 + 2x - 11
find f(x) = -6
x = 1 or -5/3 (-1.666...)
The a in a + bi
The real part of the complex number
What is the formula for completing the square?
y - x2 + bx + (b/2)2
Find the vertex for the parabola y = x2 + 8x + 21
(-4, 5)
Simplify the square root of -351
18.734...i
Find a particular equation for a parabola that has points (0, 5), (2, 13), (3, 26)
y = 3x2 - 2x + 5
What is vertex form?
y - k = a(x - h)2
What part of the equation tells you whether or not the quadratic equation has real solutions or imaginary ones?
The Discriminant
Find the x intercepts for y = x2 + 8x + 21
There are no x-intercepts - double points if you can tell me what this means in the graph of this parabola
Solve for x
x2 - 10x + 26 = 0
5 +/- i
Find the particular equation of the quadratic function containing the given ordered pairs:
(-3, 18), (6, -9), (12, -57)
y = -1/3x2 - 2x + 15
What is the Quadratic Formula
Quadratic formula
What is the formula for finding the x-coordinate for the vertex of a parabola?
h = -b/2a
Sketch the graph of a parabola whose vertex is (3, 4) and x - intercept of 1. Then write the equation for this parabola.
See graph y = -x2 - 3x - 2
Solve for x
3x(x + 5) + 2x2 = 8x - 11
-7 +/- square root of 171 i/10
-0.7 + 1.307...i -0.7 - 1.307..i
Write a particular equation of the quadratic function containing the given ordered pairs.
Vertex at (-2, 3), also containing (4, 12)
y = 1/4x2 + x + 4