3-2.

Slides:



Advertisements
Similar presentations
Solving Quadratic Equations Quadratic Formula Medina1.
Advertisements

solution If a quadratic equation is in the form ax 2 + c = 0, no bx term, then it is easier to solve the equation by finding the square roots. Solve.
EXAMPLE 4 Choose a solution method Tell what method you would use to solve the quadratic equation. Explain your choice(s). a. 10x 2 – 7 = 0 SOLUTION a.
Essential Question: What are some things the discriminate is used for?
Simplifying a Radical Review Simplify each radical and leave the answer in exact form
Notes Packet 10: Solving Quadratic Equations by the Quadratic Formula.
Solving Quadratic Equations Section 1.3
4.8: Quadratic Formula HW: worksheet
Get out Homework 9-6 Practice B Answers , , 2.48
Essential Question: How do you use the quadratic formula and the discriminant? Students will write a summary including the steps for using the quadratic.
2.6 Solving Quadratic Equations with Complex Roots 11/9/2012.
ANSWER 3. Evaluate the expression. Warm Up for Lesson x 2 when x = 4 ANSWER 128 ANSWER –1 2.–4 + x when x = 9 √ Find the (1)Axis of Symmetry, (2)the.
5.9 The Quadratic Formula 1/30/2013. Quadratic Formula: Is used to solve quadratic equations that cannot be solved using the “Big X” method. The equation.
The Quadratic Formula Students will be able to solve quadratic equations by using the quadratic formula.
Solving Quadratic Equations – Quadratic Formula The following shows how to solve quadratic equations using the Quadratic Formula. A quadratic equation.
Notes Over 5.6 Quadratic Formula
4.8 “The Quadratic Formula” Steps: 1.Get the equation in the correct form. 2.Identify a, b, & c. 3.Plug numbers into the formula. 4.Solve, then simplify.
Deriving the Quadratic Formula. The Quadratic Formula The solutions of a quadratic equation written in Standard Form, ax 2 + bx + c = 0, can be found.
Warm-Up Exercises EXAMPLE 1 Standardized Test Practice What are the solutions of 3x 2 + 5x = 8? –1 and – A 8 3 B –1 and 8 3 C 1 and – 8 3 D 1 and 8 3 SOLUTION.
ALGEBRA – LESSON 119 Quadratic Formulas Be ready to grade the homework!
3.4 Chapter 3 Quadratic Equations. x 2 = 49 Solve the following Quadratic equations: 2x 2 – 8 = 40.
Algebra Final Review Practice Problems. Factor completely.
Section 2.5 – Quadratic Equations
The Quadratic Formula..
Do Now Use the standard form of a quadratic equation to find the a, b and c of each equation. ax2 + bx + c = 0 x2 – 6x + 10 = 0 2x2 + 3x + 4 = 0 x2 –
5.6 Quadratic Formula & Discriminant
Discriminant and Quadratic
Using the Quadratic Formula to Find Solutions
Chapter 4 Quadratic Equations
Warm-up 1. Solve the following quadratic equation by Completing the Square: 2x2 - 20x + 16 = 0 2. Convert the following quadratic equation to vertex.
The Quadratic Formula..
Completing the Square of x2 + bx + c
Solve a quadratic equation
Section 5-3: X-intercepts and the Quadratic Formula
Solve each of the quadratic functions: x2 – 4 = 0 2. x2 - 2x – 8= 0
Lesson 9.3 Using the Quadratic Formula to solve equations
Review for Test: Solving
Worksheet Key 9 11/14/2018 8:58 PM Quadratic Formula.
Solving Using Quadratic Equations
The Quadratic Formula..
Find the x coordinate using -b/2a, then find the y coordinate.
9.5 Quadratic Formula.
Warmup 1. Solve x2 – 14x + 9 = 0 by completing the square.
2.2: Solving Equations Through Various Methods
4.8 The Quadratic Formula and the Discriminant
Warm Up Solve each of the quadratic functions: x2 – 3 = 0
Skills Check ALL Factoring
Questions over HW?.
The Quadratic Formula.
E) Quadratic Formula & Discriminant
5.9 The Quadratic Formula 12/11/2013.
Warm Up Solve: (x – 4)(2x – 1) = 0 2. Solve: x² – 9x = 36.
Warm Up ~ Unit 2 Day 1 Given x2 + 5x + 6 =0… Factor:
Warm-Up Day 6 Solve each of the quadratic functions by graphing and algebraic reasoning: 1. x2 – 3 = 0 2. x2 +5x – 8= 0.
Review: Simplify.
Section 9.5 Day 1 Solving Quadratic Equations by using the Quadratic Formula Algebra 1.
Solving Quadratic Equations by the Quadratic Formula
Skills Check Solve by Factoring and Square Roots
Questions over HW?. Skills Check Radical Operations and Solving by Square Roots after HW Check.
Converting Between Standard Form and Vertex Form
Warm Up #4 1. Write 15x2 + 6x = 14x2 – 12 in standard form. ANSWER
Solve quadratic equations using the: QUADRATIC FORMULA
Warm-up  .
Quadratic Formula & Discriminant
The Quadratic Formula..
Warm Up ~ Unit 2 Day 1 Solve by factoring: 3
The Quadratic Formula..
quadratic formula. If ax2 + bx + c = 0 then
Presentation transcript:

3-2

Solve 2x2 − 13x + 15 = 0 for x Do Now 3/2 Hint: factor! Essential Question: What is the quadratic formula?

Agenda Do Now Good Things Review Complex numbers Simplifying imaginary numbers Notes: Quadratic Formula Worksheet / exit ticket

GOOD THINGS

Review: Simplifying i i95 = i3 = -i We KNOW that i4 = 1. ALWAYS. To simplify: Divide (÷) the exponent by 4 The remainder is my new exponent i95  95÷4 = 23.75, or 23 remainder 3 i95 = i3 = -i

Simplifying i (6 - 6i)(8 – 2i)

Notes: Quadratic formula A quadratic equation has a squared (x2) term Standard form: ax2 + bx + c = 0 Vertex form: a(x – h)2 + k = 0 The solutions tell us the x-intercepts We use factoring, completing the square, and the quadratic formula to find the solutions

Quadratic formula

quadratic formula Step 1: Make sure equation is in standard form Step 2: Identify a, b, and c Step 3: Plug in a, b, and c (CAREFUL WITH THE NEGATIVES!) Step 4: Simplify

quadratic formula x2 + 2x = 3 Standard form: ax2 + bx + c = 0 IF you cannot factor, plug a, b, and c into the quadratic formula x2 + 2x = 3

Quadratic formula 3x2 -10x = - 5 It’s okay to leave answers in radical form!

quadratic formula 4x2 + 11x -20 = 0 #1 on your worksheet Take 5 minutes to solve for x. 4x2 + 11x -20 = 0

Quadratic Formula Worksheet Due at the end of class MUST SHOW WORK – cannot just put final results Staple any paper you use Reminder: Independent Practice is due tomorrow at the start of class