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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