Warm Up Test Friday HW- Solving Quadratics Worksheet

Homework Check

Lesson: Solving Quadratics February 11, 2014

Now we are going to talk about quadratic equations Recall…….. What have we learned so far about quadratic functions? Now we are going to talk about quadratic equations The standard form of a quadratic equation is 𝒂𝒙 𝟐 +𝒃𝒙+𝒄 =0

Solving Quadratic Equations Quadratic equations can be solved by a variety of methods, including graphing and finding square roots. When solving the quadratic equation( 𝒂𝒙 𝟐 +𝒃𝒙+𝒄=𝟎 ) by graphing the solutions of the equation are the x-intercepts of the related function. We have talked about x-intercepts before in our unit on functions, what can you recall about x-intercepts?

Solving by Graphing The solutions of a quadratic equation and the x-intercepts of the graph of the related function are often called roots of the equation or zeros of the function. Let’s practice finding the solutions by graphing

Solving by factoring We have just learned many ways to factor polynomials in the standard form 𝒂𝒙 𝟐 +𝒃𝒙+𝒄, we can also use this to help us find solutions. Let’s factor the following 𝒙 𝟐 −𝟏𝟔 If you recall the standard form of a quadratic equation is 𝒂𝒙 𝟐 + 𝒃𝒙+𝒄=𝟎all we have to do is set our answer to zero and solve for x to get our zeros. (Can you see where they got the term zero from)

Solving by Factoring We can use something called the zero-product property to help us find the zeros. Let’s use the problem we just factored and set equal to zero. Using the zero product property

Using the Zero-Product Property What are the solutions of the following equations? (4t + 1) (t – 2 )=0 (x + 1)(x – 5)= 0 (2x + 3)(x – 4)=0 (7n - 2)(5n – 4)=0

Solving by Factoring Factor and solve the following to find the solutions 𝑥 2 +8𝑥+15=0 What about this one? 4𝑥 2 −21𝑥=18

Solving by Using Square Roots You can solve equations of the form 𝑥 2 =𝑘 by finding the square roots of each side. Example: 3𝑥 2 −75=0

Solve by Using Square Roots What are the solutions of each equation? 𝑚 2 −36=0 3𝑥 2 +15=0 4𝑑 2 +16=16

Independent Practice Time Time to do more problems without me!!!

Exit Ticket What are the solutions to the following? 3𝑥 2 −27𝑥+54=0