Evaluating Quadratic Functions (5.5) Figuring out values for y given x Figuring out values for x given y.

Slides:

Advertisements

Similar presentations

Complex Numbers.

Advertisements

12-4 Quadratic Functions CA Standards 21.0 and 22.0 CA Standards 21.0 and 22.0 Graph quadratic functions; know that their roots are the x-intercepts; use.

Quadratic Equations From Their Solutions From solutions to factors to final equations (10.3)

Quadratic Equations and Quadratic Functions Review.

If b2 = a, then b is a square root of a.

Complex Number A number consisting of a real and imaginary part. Usually written in the following form (where a and b are real numbers): Example: Solve.

Solving Quadratic Equations

11.1 Solving Quadratic Equations by the Square Root Property

Unit 5 Quadratics. Quadratic Functions Any function that can be written in the form.

The Roots of a Quadratic Equation. What are the zeros/roots? They are where the arms of a parabola cross the x-axis, and y is zero. There can be two zeros,

Solving Quadratic Equations (finding roots) Example f(x) = x By Graphing Identifying Solutions Solutions are -2 and 2.

Chapter 7 Quadratic Equations and Functions

Sec 5.6 Quadratic Formula & Discriminant Quadratic Formula (Yes, it’s the one with the song!) If ax 2 + bx + c = 0 and a ≠ 0, then the solutions (roots)

Objectives: To solve quadratic equations using the Quadratic Formula. To determine the number of solutions by using the discriminant.

Warm up – Solve by Taking Roots. Solving by the Quadratic Formula.

Quadratic Equations, Functions, and Models

Objectives Define and use imaginary and complex numbers.

Factoring Finding factors given a Graph Medina1. Finding factors given a Graph *Note: If the function only has one x-intercept, there is not two different.

Fireworks – Finding Intercepts

Algebra 1B Chapter 9 Solving Quadratic Equations The Discriminant.

5.6 Quadratic Equations and Complex Numbers

Fundamental Theorem of Algebra If f(x) is a polynomial of degree n, where n≥1, then the equation f(x) = 0 has at least one complex root. Date: 2.6 Topic:

Solving Quadratic Equations

Objective - To use the discriminant to determine the number of real solutions for a quadratic. Quadratic FormulaDiscriminant Used to find the roots of.

Math is about to get imaginary!

5.3 x-intercepts and the Quadratic Formula Building on what we did last time (What have we looked at so far?)

UNIT 3 Stuff about quadratics. WHAT DO YOU DO IF YOU SEE A NEGATIVE UNDER THE RADICAL?

Review How do we solve quadratic equations? 1.) Factoring using “Bottoms Up” 2.) if its not factorable by “Completing the Square”

3.8 Warm Up Write the function in vertex form (by completing the square) and identify the vertex. a. y = x² + 14x + 11 b. y = 2x² + 4x – 5 c. y = x² -

Quadratic Formula & Discriminant

X-Intercepts/Roots: Discriminant and the Quadratic Formula 1. Review: X-Intercepts are the Roots or Solutions x y Y = f(x) = 0 at the x-intercepts (curve.

5.9.1 – The Quadratic Formula and Discriminant. Recall, we have used the quadratic formula previously Gives the location of the roots (x-intercepts) of.

Discriminant Recall the quadratic formula: x = -b ±√ b2 - 4ac 2a.

Solving Quadratic Functions Lesson 5-3. Objective Today, you will... solve quadratic functions by using a variety of methods. TEKS:b2A,d1A,d3A,d3C,d3D.

The Quadratic Formula & Discriminant Essential question – How do you solve a quadratic equation using the Quadratic Formula?

5.6 – Quadratic Equations and Complex Numbers Objectives: Classify and find all roots of a quadratic equation. Graph and perform operations on complex.

What you will learn How to solve a quadratic equation using the quadratic formula How to classify the solutions of a quadratic equation based on the.

Graphing Polynomials. Total number of roots = __________________________________. Maximum number of real roots = ________________________________. Maximum.

Pre-Calculus Lesson 5: Solving Quadratic Equations Factoring, quadratic formula, and discriminant.

Quadratic Formula You can use this formula to find the solutions(roots) to a quadratic equation. This formula can be broken up into 2 parts: b 2 – 4ac.

The Quadratic Formula Students will be able to solve quadratic equations by using the quadratic formula.

By: Adam Linnabery. The quadratic formula is –b+or-√b 2 -4ac 2a an example of how it is used: X 2 -4x-12=0 the coefficient of x 2 is 1 therefore the value.

Bell Work Solve the Equation by Factoring or using Square Roots: Solve the equation by using the quadratic formula: 3. Identify the parts of a parabola:

$200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400.

How to solve Quadratic Equations By John Jackson.

Given a quadratic equation use the discriminant to determine the nature of the roots.

Jeff Bivin -- LZHS Quadratic Equations. Jeff Bivin -- LZHS Convert to Standard Form f(x) = 5x x + 46 f(x) = 5(x 2 - 8x + (-4) 2 ) f(x)

UNIT 4 Stuff about quadratics. WHAT DO YOU DO IF YOU SEE A NEGATIVE UNDER THE RADICAL?

Real and Complex Roots 20 October What is a root again?

9.2 THE DISCRIMINANT. The number (not including the radical sign) in the quadratic formula is called the, D, of the corresponding quadratic equation,.

Real Zeros of Polynomial Functions. Solve x 3 – 2x + 1 = 0. How? Can you factor this? Can you use the quadratic formula? Now what if I tell you that one.

Bellwork Perform the operation and write the result in standard from ( a + bi)

 Real roots can be found from the graph (x-intercepts)  We use synthetic division with the real roots to solve for the imaginary roots  There are as.

Section )by graphing (using the calculator to identify the roots (x-intercepts)) 2)by factoring 3)by “completing the square” 4)by Quadratic Formula:

Complex Numbers Quadratic Formula Completing The Square Discriminant.

Warm UP Take a few minutes and write 5 things you remember about the quadratic formula?? Take a few minutes and write 5 things you remember about the quadratic.

Imaginary and Complex Numbers (5.4) Roots when the Discriminant is negative.

ALGEBRA 1 SECTION 10.7 Interpret the Discriminant Big Idea: Determine the number of solutions to a quadratic equation. Essential Question: How do you use.

Key Components for Graphing a Quadratic Function.

SOLVE QUADRATIC EQUATIONS BY USING THE QUADRATIC FORMULA. USE THE DISCRIMINANT TO DETERMINE THE NUMBER AND TYPE OF ROOTS OF A QUADRATIC EQUATION. 5.6 The.

Characteristics of Quadratic Functions CA 21.0, 23.0.

Warm up – Solve by Taking Roots

Objectives Define and use imaginary and complex numbers.

Introductory Algebra Glossary

The Quadratic Formula..

Daily Check!!! (Irrational Roots)

Warm up – Solve by Completing the Square

1. Use the quadratic formula to find all real zeros of the second-degree polynomial

Homework Check.

Presentation transcript:

Evaluating Quadratic Functions (5.5) Figuring out values for y given x Figuring out values for x given y

First a little POD What is the complex conjugate of i? What is their product? What is the complex conjugate of m + ni? What is their product?

For f(x) = 3x 2 + 2x -11 Find f(-4). Find the x-intercepts.

For f(x) = 3x 2 + 2x -11 f(-4) = 3(-4) 2 + 2(-4) -11 = 29 Find the x-intercepts. How would we show them in (x, y) form?

For f(x) = 3x 2 + 2x -11 Find x, if f(x) = 6. Hint: how do you set this up?

For f(x) = 3x 2 + 2x -11 Find x, if f(x) = 6. Set the y side equal to 0, and use the quadratic formula. Because the discriminant is a non- negative number, we will have real roots.

For f(x) = 3x 2 + 2x -11 Will f(x) ever equal -5? Will it ever equal -15?

For f(x) = 3x 2 + 2x -11 Will f(x) ever equal -5? Again, we can tell this is possible because of the discriminant.

For f(x) = 3x 2 + 2x -11 Will it ever equal -15? In this case, a negative discriminant tells us that this is not possible– the graph does not reach down to -15.

For f(x) = 3x 2 + 2x -11 Graph the parabola on your calculators. Does the parabola ever cross the line y = -5 or the line y = -15?

For f(x) = 3x 2 + 2x -11 Graph the parabola on your calculators. Does the parabola ever cross the line y = -5 or the line y = -15?