Warm-Up Solve the following quadratic equations

Homework

Still do not get how to solve quadratic equations? Let’s take 10 minutes to do the scavenger hunt for more practice.

Lesson: Graphing Quadratic Equations February 17, 2014

Recall………Quadratic Equations So far we have learned… What a quadratic equation is How a quadratic equation is shaped What the parent equation of a quadratic equation looks like How we can transform(move) quadratic equations and How to solve quadratic equations

More on Quadratic Equations In today's lesson we will discuss more features of the quadratic equation and how to find them such as Axis of Symmetry, and tomorrow we will learn how to graph a quadratic equation.

How does it look? We know that the Quadratic Parent Equation is ? We also know that the shape of the graph of a quadratic equation is a ______________? If you fold the parabola in half to get two equal sides. The line splitting the two halves is called the axis of symmetry Later in this lesson we will introduce a formula for the Axis of Symmetry

Examining the Graph of a Parabola Fill in the Blanks We have learned that the ____________and the Max/Min are the same point. If asked for the Max/Min value that would be the________________________. The Axis of symmetry is the x-coordinate of the Vertex(Max/Min).

Before we can start to graph here is a visual of all the things you need to know

Parts of the Graph Vertex: Max or min value: the y-value of the vertex Highest point (maximum) Lowest point (minimum) Max or min value: the y-value of the vertex Axis of symmetry: the x-value of the vertex

Info from equation Direction of opening: If a>0, the direction of opening is UP and the vertex would be a minimum. If a<0, the direction of opening is DOWN and the vertex would be a maximum. Example: y = 5x2 + 10x – 7

Info from equation Y-intercept: in standard form, c gives us the y-intercept. y = ax2 + bx + c Example: y = 5x2 + 10x – 7

Give the direction of opening and y-intercept of the following: y = -8x2 + 2x + 1 y = 6x2 – 24x - 4

Practice

How can we find the vertex of a parabola if we are not given a graph?

This is where the Axis of Symmetry comes in! Recall - The line splitting the two halves of a parabola is called the axis of symmetry and the A.O.S is the x-coordinate of the Vertex(Max/Min). So if we know the x-coordinate then we can plug that into our equation to get the y coordinate

Using the Axis of Symmetry Formula for the AOS: Always starts with x = This indicates that it is a vertical line Will always be x = #

Find the Axis of symmetry for the following quadratic equations 1) y = x2 – 2x – 3 a = ____, b = ____, c = ____ 2) y = -2x2 + 8x – 5 a = ____, b = ____, c = ____ 3) y = -x2 + 2x + 2 a = ____, b = ____, c = ____

Now let’s use those same problems to find the Vertex. 1) y = x2 – 2x – 3 x = ____ Vertex: ( , ) 2) y = -2x2 + 8x – 5 3) y = -x2 + 2x + 2

Can this be done using the calculator? Yes Let’s find the vertex of the following quadratic equation and state whether it is a maximum point or minimum point.

More Practice Using the Calculator Find the vertex of the following quadratic equations and state whether it is a maximum point or minimum point.

Homework Finding the Axis of Symmetry and Vertex using A.O.S