THINGS YOU NEED TO KNOW HOW TO DO FROM CHAPTER 5
THINGS YOU NEED TO KNOW HOW TO DO FROM CHAPTER 5
SECTION 5.1:
Graph a quadratic in all 3 forms: standard, vertex, and intercept.
Standard form: [pic]
y-intercept: (0,c)
vertex: x coordinate found by [pic], substitute that x into equation to find y.
x-intercept(s): let y = 0, solve by factoring, quadratic formula, or square-rooting.
Opens up if a is positive, opens down if a is negative.
Vertex form: [pic]
vertex: ( h , k ) Note: do the opposite of what is inside the parenthesis, outside is what it says.
y-intercept: let x = 0 in the equation, solve for y.
x-intercept(s): let y = 0, solve for x.
Intercept form: [pic]
x-intercepts: (p , 0) and (q , 0)
vertex: x coordinate found by going half way between the x-intercepts. y coordinate found by substituting that x into the equation.
y-intercept: let x = 0 in the equation, solve for y.
Change from vertex or intercept form to standard form: FOIL the parenthesis and combine like terms.
Application problems. The minimum value of a quadratic is found at the y-coordinate of the vertex that opens up. The maximum value is found at the y-coordinate of the vertex that opens down.
SECTION 5.2
Factor a quadratic expression.
Solve a quadratic equation in standard form by factoring, setting each factor equal to zero.
SECTION 5.3
Simplify a square root, and rationalize the denominator if it is irrational.
Solve a quadratic equation by taking the square root of both sides, remembering to put [pic]on the right side.
SECTION 5.4
Complex numbers: [pic]
Standard form of a complex number: [pic]
Add and subtract complex numbers: combine like terms, the real parts together and the imaginary parts together.
Multiply complex numbers: FOIL and combine like terms. Remember to simplify [pic] to be -1 and combine it with the constant term.
Divide complex numbers: multiply numerator and denominator by the complex conjugate of the denominator to get the denominator to be real.
Graph a complex number in the complex plane: plot the point as ( a , b ).
Find the absolute value of a complex number: [pic]
SECTION 5.5
Complete the square to solve a quadratic in standard form.
Steps: 1) Make sure a = 1. If not, divide through by a to make it 1.
2) Move the constant to the other side of the equation.
3) Divide b by 2.
4) Add [pic] to both sides of the equation.
5) Rewrite the left side to [pic], simplify the right side.
6) Take the square root of both sides, remembering to put [pic]on the right side.
7) Solve for x.
SECTION 5.6
Solve a quadratic equation in standard form by using the quadratic formula.
[pic], where a, b, and c are found in standard form = 0.
Use the Discriminant to determine the number and type of solutions to a quadratic.
[pic]
If D = 0, then 1 real solution.
If D > 0, then 2 real solutions.
If D < 0, then 2 imaginary solutions.
Use the height of a dropped object equation: [pic], where h is the height after t seconds, t is the time after the object was dropped (in seconds), and [pic] is the initial height (the height of the object when it was dropped).
Use the height of a thrown (or launched) object equation: [pic], where all of the variables are the same as above and [pic] is the initial velocity (the speed the object was traveling at when it was thrown).
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