Math 3rd periodical exam

Quadratic equation Extracting the square root Completing the square Factoring Using the Quadratic formula SUM of ROOTS of QUADRATIC EQUATION PROBLEM SOLVING RATIONAL EQUATION MOTION PROBLEMS Quadratic Inequality

2

Degree is the highest exponent of a given polynomial expression. What is the degree of a quadratic equation?

Two real equal

The equation 4x² - 20x + 25 has discriminant equal to 0. If the discriminant is equal to 0, what is the nature of the root of he quadratic equation?

d= b² - 4ac

The discriminant is the one to determine whether the roots are real equal, real unequal, and imaginary. What is the formula for the discriminant?

ax² +bx +c = 0

A quadratic equation has two forms, the general from and the standard form. What is the general form of a quadratic equation?

Rational and unequal

The discriminant is greater than 0 and a perfect square. What is the nature of the root of the quadratic equation?

Two real unequal

The discriminant determines the nature of the roots of a quadratic equation. What is the nature of the discriminant of the quadratic equation below?

Two imaginary

The discriminant is less than 0 but not a perfect square. What is the nature of the root of the quadratic equation?

I only

A quadratic equation has a highest degree of 2. Which of the examples below is/are quadratic equation?

x= +5

Getting the square root is one way of getting the roots of a quadratic equation. Given x² = 25,what is the value of x?

x² - 4 = 0

Simplify : (x - 2)(x + 2)= 0

a = 5

Determine a of 2x + 5x² = -2

b = 2

Determine b of 2x + 5x² = -2

c = 2

Determine c of 2x + 5x² = -2

a = 3

Determine a of 3x² - 9 + 40 =0

b = -9

Determine b of 3x² - 9 + 40 =0

c = 40

Determine a of 3x² - 9 + 40 =0

a = 5

Determine a of 10x + 20 = -5x²

b = 10

Determine b of 10x + 20 = -5x²

c = 20

Determine c of 10x + 20 = -5x²

a = 4

Determine a of 4x (x - 12) + 21 = 0

b = -48

Determine b of 4x (x - 12) + 21 = 0

c = 21

Determine c of 4x (x - 12) + 21 = 0

a = 2

Determine a of 2x (x + 5) + 7 = 0

b = 10

Determine b of 2x (x + 5) + 7 = 0

c = 7

Determine c of 2x (x + 5) + 7 = 0

C

Directions: identify the nature of roots of each quadratic equation. Put (A) if the roots are real and distinct, (B) if the roots are real and equal, and (C) if the roots are imaginary.

x² - 3x - 1 = 0

B

Directions: identify the nature of roots of each quadratic equation. Put (A) if the roots are real and distinct, (B) if the roots are real and equal, and (C) if the roots are imaginary.

x² - 4x +4 = 0

C

Directions: identify the nature of roots of each quadratic equation. Put (A) if the roots are real and distinct, (B) if the roots are real and equal, and (C) if the roots are imaginary.

2x² - 6x - 3 = 0

C

Directions: identify the nature of roots of each quadratic equation. Put (A) if the roots are real and distinct, (B) if the roots are real and equal, and (C) if the roots are imaginary.

x² + x + 2 = 0

A

Directions: identify the nature of roots of each quadratic equation. Put (A) if the roots are real and distinct, (B) if the roots are real and equal, and (C) if the roots are imaginary.

4x² - 5x - 7 = 0

Extracting Square Roots

Directions: Factor completely and solve for the values of x and identify if it is (FACTORING, COMPLETING THE SQUARE, EXTRACTING SQUARE ROOTS, QUADRATIC FORMULA)

x² - 1 = 0

Factoring

Directions: Factor completely and solve for the values of x and identify if it is (FACTORING, COMPLETING THE SQUARE, EXTRACTING SQUARE ROOTS, QUADRATIC FORMULA)

x² - 3x - 4 = 0

Quadratic Formula

Directions: Factor completely and solve for the values of x and identify if it is (FACTORING, COMPLETING THE SQUARE, EXTRACTING SQUARE ROOTS, QUADRATIC FORMULA)

4x² + 18x + 14 = 0

Extracting Square Roots

Directions: Factor completely and solve for the values of x and identify if it is (FACTORING, COMPLETING THE SQUARE, EXTRACTING SQUARE ROOTS, QUADRATIC FORMULA)

x² = 16

Completing the Square

Directions: Factor completely and solve for the values of x and identify if it is (FACTORING, COMPLETING THE SQUARE, EXTRACTING SQUARE ROOTS, QUADRATIC FORMULA)

x² - 4 = 21

Quadratic Formula

Directions: Factor completely and solve for the values of x and identify if it is (FACTORING, COMPLETING THE SQUARE, EXTRACTING SQUARE ROOTS, QUADRATIC FORMULA)

2x (x + 10) = 56

Square

The name quadratic comes from "quad” meaning?

Quadratic equation

The equation where the highest exponent of the variable is “usually” a square of (²)

Extracting the square root
Completing the square
Factoring
Using the Quadratic Formula

What are the 4 ways in solving Quadratic equation?

Extracting the square root

___ involves isolating the square and then applying the square root property.

(bx/2)²

What is the formula for Completing the square?

Factoring

When constant is 0, the quadratic equation will be of the form ax² + bx = 0

x= -b±√(b²-4ac))/(2a) .

What is the formula for Quadratic formula?

_{X1 + X2 = -b/a}

Formula for SUM of Roots

X1 x X2 = -c/a

Formula for PRODUCT of Roots

Sum: -8 / 2 = -4

Find the SUM of the roots

2x² + 8x - 10 = 0

Product: 10 / 2 = 5

Find the Product of the Roots

2x² + 8x - 10 = 0

So that finding the roots is easier.

What is the use of getting the sum and the product of the roots?

Rational Equation

___ is an equation containing at least one fraction whose numerator and denominator are polynomials. In symbols P(x) / Q(x)

Greater than

Term for ( >)

Less than

Term for (<)

Greater than or equal to

Term for ( > )

Less than or equal to

Term for ( < )

Solution not included

Interval Notation for the solutions set
(>) (<) Parenthesis and not shaded circle meaning?

Solution included

Interval Notation for the solutions set
(>) (<) Brackets and shaded circle meaning?

3 steps

How many steps in Quadratic Inequality?

Step 1: Express the quadratic inequalities a quadratic equation
Step 2: Equate the 0 and solve for x.
Locate on the number line.
Step 3: Choose a point test

What are the 3 steps in solving Quadratic Inequality?

Christine Macawili

Tcher Chris’s full name?

1 and 4

Factor of 5 and 4