FINDING THE EQUATION OF A QUADRATIC FUNCTION Foldable.

Slides:

Advertisements

Similar presentations

Solve a System Algebraically

Advertisements

EXAMPLE 6 Write a quadratic function in vertex form Write y = x 2 – 10x + 22 in vertex form. Then identify the vertex. y = x 2 – 10x + 22 Write original.

How do I write quadratic functions and models? 7.2 Write Quadratic Functions and Models Example 1 Write a quadratic function in vertex form Write a quadratic.

1 of 7 Pre-Calculus2 Chapter 10 Section 8 Warm up Write the equation in standard form of Write the equation in standard form of Then find the coordinates.

Solving Equations In Quadratic Form There are several methods one can use to solve a quadratic equation. Sometimes we are called upon to solve an equation.

Solve an equation with variables on both sides

1.The standard form of a quadratic equation is y = ax 2 + bx + c. 2.The graph of a quadratic equation is a parabola. 3.When a is positive, the graph opens.

Graph an equation of a parabola

5.1 Quadratic Function 11/30/12. Graph is a parabola Vocabulary Quadratic Function : a function that is written in the standard form: y = ax 2 + bx +

Table of Contents Solving Equations In Quadratic Form There are several methods one can use to solve a quadratic equation. Sometimes we are called upon.

Write a quadratic function in vertex form

Algebra 2 (Section 4.9).

EXAMPLE 1 Write a quadratic function in vertex form Write a quadratic function for the parabola shown. SOLUTION Use vertex form because the vertex is given.

Solving quadratic equations by graphing. X Y I x² - 2x = 3 You have to rewrite the equation to find the vertex before you can graph this function Use.

Completing the Square 4-6 Day 1 Today’s Objective: I can use the process of completing the square to solve or rewrite a quadratic equation.

Finding a Quadratic Equation from Three Coordinates.

Learning Task/Big Idea: Students will learn how to find roots(x-intercepts) of a quadratic function and use the roots to graph the parabola.

9.3 Graphing Quadratic Functions

Sec. 5-3: Translating Parabolas. We will write equations of parabolas using the VERTEX FORM when given the VERTEX and one other point: Y = a(x – h) 2.

Use Linear Equations in Slope Intercept Form. Given a Slope and Coordinate Define the variables we know – m, (x, y) Substitute into slope intercept form.

1.The standard form of a quadratic equation is y = ax 2 + bx + c. 2.The graph of a quadratic equation is a parabola. 3.When a is positive, the graph opens.

Solving Quadratic Equations – Quadratic Formula The following shows how to solve quadratic equations using the Quadratic Formula. A quadratic equation.

Graphing & Solving Quadratic Inequalities 5.7 What is different in the graphing process of an equality and an inequality? How can you check the x-intercepts.

EXAMPLE 1 Solve an equation with two real solutions Solve x 2 + 3x = 2. x 2 + 3x = 2 Write original equation. x 2 + 3x – 2 = 0 Write in standard form.

Learning Task/Big Idea: Students will learn how to graph quadratic equations by binding the vertex and whether the parabola opens up or down.

FACTORING a). FACTORING a) FACTORING a) FACTORING a)

Focus and Directrix 5-4 English Casbarro Unit 5: Polynomials.

Advanced Algebra Notes Section 4.9: Graphing Quadratic Inequalities A _________________________________ can be written as follows: Remember when graphing.

3.2 Solving Systems Algebraically When you try to solve a system of equations by graphing, the coordinates of the point of intersection may not be obvious.

ONE STEP EQUATIONS Multiplication and Division ONE STEP EQUATIONS Example 1 Solve 3x = 12 Variable? x 3x = 12 x x 3 ÷ 3 Inverse operation? Operation?

Algebra Review. Systems of Equations Review: Substitution Linear Combination 2 Methods to Solve:

10.3 Solving Quadratic Equations – Solving Quadratic Eq. Goals / “I can…”  Solve quadratic equations by graphing  Solve quadratic equations using.

Objective: Use factoring to solve quadratic equations. Standard(s) being met: 2.8 Algebra and Functions.

Algebra Completing the Square. Solving with Square Roots.

Write a quadratic function in vertex form

How To Graph Quadratic Equations Standard Form.

Coefficients a, b, and c are coefficients Examples: Find a, b, and c.

3.4 Solving Systems with 3 variables

Graphing Quadratic Inequalities

Graphing and solving quadratic inequalities

Quadratic and Other Nonlinear Inequalities

1.The standard form of a quadratic equation is y = ax 2 + bx + c. 2.The graph of a quadratic equation is a parabola. 3.When a is positive, the graph opens.

How to Graph Quadratic Equations

Translating Parabolas

How To Graph Quadratic Equations

Academy Algebra II 4.7: Completing the Square

Graph and Solve Quadratic Inequalities

4.10 Write Quadratic Functions and Models

Section 9.4 Day 1 Solving Quadratic Equations by Completing the Square

Systems of Linear and Quadratic Equations

How To Graph Quadratic Equations.

Quadratic Functions & Models

You can find the roots of some quadratic equations by factoring and applying the Zero Product Property. Functions have zeros or x-intercepts. Equations.

Solving One Step Equations

Solving Equations with Variables on Both Sides

Solving Equations with Variables on Both Sides

Completing the Square Algebra Review.

How To Graph Quadratic Equations.

Section 10.2 “Graph y = ax² + bx + c”

I will write a quadratic function in vertex form.

Chapter 8 Systems of Equations

Welcome Activity Pass out the WKS on:

Warm up Graph 1. y = 3x² - 6x y = -x² + 2x – 1

Notes Over 5.8 Writing a Quadratic Function in Vertex Form

5.8 Modeling with Quadratic Functions

Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

Solving Systems by ELIMINATION

y = ax2 + bx + c Quadratic Function

Write Quadratic Functions and Models

How To Graph Quadratic Equations.

Presentation transcript:

FINDING THE EQUATION OF A QUADRATIC FUNCTION Foldable

STEP 1 (INSIDE ON THE LEFT)  Find the vertex (h, k)  Find the coordinate of another point (x, y) on the parabola

STEP 1 (INSIDE ON THE RIGHT)  Vertex = (1,0)  h = 1  K = 0  Pick a point: = (2, 1)  X = 2  Y = 1

STEP 2 (INSIDE ON THE LEFT)

STEP 2 ( INSIDE ON THE RIGHT)  Vertex = (1, 0)  h = 1  k = 0

STEP 3 (INSIDE ON THE LEFT)  Rewrite the equation with the (x, y) substituted in.

STEP 3 (INSIDE ON THE RIGHT)

STEP 4 (INSIDE ON THE LEFT)  Now, solve algebraically for the variable “a”!

STEP 4 (ON THE RIGHT SIDE)

STEP 5 (INSIDE ON THE LEFT)  Substitute a, h, and k into your original equation.

STEP 5 (INSIDE ON THE RIGHT) h = 1 k = 0 a = 1

STEP 6 (INSIDE ON THE LEFT)  Put your new function into simplest form.

STEP 6 (INSIDE ON THE RIGHT)