The Quadratic Formula L.O.

Slides:

Advertisements

Similar presentations

Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic Int.

Advertisements

What are you finding when you solve the quadratic formula? Where the graph crosses the x-axis Also known as: Zeros, Roots and X-intercepts.

Warmup 9-11 Solve the following equations by factoring. Show work! 1.x x - 80 = 0 2.Solve by using the quadratic formula: 4x 2 - 5x - 2 = 0 3.Solve.

Solving Quadratics. Methods for Solving Quadratics Graphing Factoring Square Root Method Completing the Square Quadratic Formula.

Theorems About Roots of Polynomial Equations. Find all zeros: f(x)= x +x –x Synthetic Division one zero…need 2 more use (x – k), where.

Quadratic Equations using the formula using the formula.

Solve by factoring. x² = - 4 – 5x 2,. Solve by factoring. n² = -30 – 11n -4 and -1.

Graphing quadratic functions part 2. X Y I y = 3x² - 6x + 2 You have to find the vertex before you can graph this function Use the formula -b 2a a = 3.

In the quadratic function x 2 – 2x + c = 0, c represents an unknown constant. If x = -6 is one of the solutions, what is the other solution?

The Quadratic Formula..

The Quadratic Formula..

Quadratic Formula Solving for X Solving for quadratic equations.

On this happy face, what quadratic function graphs a smile that

All pupils are confident with function notation including:

Solving Quadratic Equations by Graphing

Graphing Inequalities

Transformations L.O. All pupils can recall how changes in equations transform graphs of functions All pupils can confidently solve all the homework questions.

Transforming Trigonometric Graphs

Transformations on Trigonometric Graphs

All pupils can sketch a variety of graphs

Differentiation L.O. All pupils are aware of differentials of common functions All pupils can solve basic differentiation questions Some pupils can solve.

Optimisation L.O. All pupils understand how quadratics can model real life situations All pupils recognize how parts of the graph relate to the real life.

Quadratics Multiply out (x+16) (x-16) (x+12) (x-12) = ?

Trigonometric Graphs L.O.

Simultaneous Equations

Quadratic Equations L.O.

all pupils can find the area of a triangle using trigonometry

Substitution L.O. All pupils can complete simple substitutions

Exploring Quadratic Expressions

The Quadratic Formula L.O.

Roots of Quadratics L.O. All pupils understand what roots of quadratics are graphically and algebraically All pupils are confident with finding the roots.

Exploring Quadratic Expressions

Quotient Rule L.O. All pupils can solve basic differentiation questions All pupils can solve some problems requiring the Quotient Rule.

All pupils can read off the base trigonometric graphs

Composite Functions L.O.

All pupils know what polynomials are

Product Rule L.O. All pupils can solve basic differentiation questions

Functions L.O. All pupils can describe the different types of functions All pupils can find the domain and range of basic functions Some pupils can find.

Practicing Similarity and Congruence

All pupils can use circle theorems to solve a variety of questions

How does substitution help link equations and their graphs?

Quadratic Graphs.

All pupils can recall information on real life graphs

Different Types of Functions

Algebra - Brackets L.O. All pupils understand the importance of brackets Most pupils can use brackets in situations with algebra.

All pupils can define a linear equation

Exponentials and Logarithms

Algebra – Brackets 2 L.O. All pupils can expand linear expressions

More Linear Equations L.O.

Further Investigating Quadratics

The Quadratic Formula..

Rates of Change L.O. All pupils can recall information on real life graphs to both draw and visualise them All pupils can apply their knowledge of on a.

Composite and Inverse Functions

Quadratic Sequences L.O.

Quadratics L.O. All pupils can recall information about quadratic functions All pupils can answer a variety of questions about quadratic functions.

Function Notation L.O. All pupils can understand function notation

Gradients L.O. All pupils can find the gradient of linear graphs

Other ways of Describing Sequences

All pupils can recall and work with a variety of functions

Points of Intersection using Algebra

All pupils can work with arithmetic sequences

The Quadratic Formula and Factorising

All pupils can manipulate geometric sequences

The Quadratic Formula..

More Functions L.O. All pupils can recall the different types of functions All pupils can find the domain and range of basic functions Some pupils can.

What’s the same and what’s different?

quadratic formula. If ax2 + bx + c = 0 then

Difference between Expression and Equation?

Presentation transcript:

The Quadratic Formula L.O. All pupils understand when to use the quadratic formula All pupils can use the quadratic formula All pupils understand what they can find out from the number of roots

When do we use the quadratic formula? Starter: Quadratic formula usage When do we use the quadratic formula?

Starter: Quadratic formula usage We use the quadratic formula to find the roots of graphs when we cannot factorise.

What do I mean with ‘the roots of quadratics’? Starter: Quadratic formula usage What do I mean with ‘the roots of quadratics’? 𝒙 𝟐 −𝟒𝒙=𝟎

The Quadratic Formula L.O. All pupils understand when to use the quadratic formula All pupils can use the quadratic formula All pupils understand what they can find out from the number of roots

What is the quadratic formula? Main 1: use the quadratic formula What is the quadratic formula?

Find the number of roots for each of the functions Main 1: use the quadratic formula Use the quadratic formula to find where the functions on the other board cross the x axis. Ext: find out from the number of roots Find the number of roots for each of the functions

The Quadratic Formula L.O. All pupils understand when to use the quadratic formula All pupils can use the quadratic formula All pupils understand what they can find out from the number of roots

How can you find the number of roots through the quadratic formulas? Main 2: find out from the number of roots How can you find the number of roots through the quadratic formulas?

The Quadratic Formula L.O. All pupils understand when to use the quadratic formula All pupils can use the quadratic formula All pupils understand what they can find out from the number of roots

Plenary: Wipeboards

The Quadratic Formula L.O. All pupils understand when to use the quadratic formula All pupils can use the quadratic formula All pupils understand what they can find out from the number of roots