Chapter 5 Test (5-1 through 5-8)
Equation with Rational Roots
-Factor they perfect square trinomial -Square Root Property -Find the square root -Solve the equation using the positive and negative
Factored Form
0 = a(x - p) (x - q)
Graph a Quadratic Inequality
1.) Graph the Function 2.) Test a point 3.) If point is a solution shade area that includes the point/If point isn't a solution shade area that doesn't includes the point
Complex Numbers
Any number can be written in the form a + b*i*
Quadratic Inequalitites
Can graph in two variables by using the same techniques used to graph linear inequalities in two variables
Imaginary Unit (i)
Defined as *i*² = -1 *i* = √-1
Quadratic Function
In a quadratic function the greatest exponent is 2
Axis of Symmetry
Line through the graph of a parabola that divides the graph into two congruent halves
Zeros
One method for finding the roots of a quadratic equation is to find the zeroes of the quadratic function
Square Root Property
Putting the +/- in front of the radical
Quadratic Equation
Quadratic functions that are set equal to 0
Solve Quadratic Inequalities
Quadratic inequalities in one variable can be solved using the graphs of the related quadratic functions
Write an Equation Given Roots
Replace p and q with the roots [0 = a(x - p) (x - q)] Foil and simplify
Roots
Solutions of a quadratic equation
Pure Imaginary Numbers
Square roots of negative real numbers For any positive real number b, √-b² = √b² × √-1 or b*i*
Constant Term
Term in a quadratic function with no x term
Linear Term
Term in a quadratic function with the x term
Quadratic Term
Term in a quadratic function with the x² term
Vertex
The axis of symmetry will intersect a parabola at only one point
FOIL Method
Uses the Distributive property to multiply binomials
Maximum Value
Y-value of the vertex of a quadratic function (downwards opening)
Minimum Value
Y-value of the vertex of a quadratic function (upwards opening)
Standard Form
ax² + bx + c = 0 (a does not equal 0, a b and c are integers)
Discriminant
b² − 4ac (the part of the Quadratic formula under the square root) Can be used to determine the number and types of solutions
Vertex Form
y = a (x - h)² + k where (h, k) is the vertex x = h is the axis of symmetry a is the shape of the parabola