Section 2.2 Characteristics of Quadratic Functions Honors Algebra 2 Section 2.2 Characteristics of Quadratic Functions

Essential Question What is symmetry?

Why is the paper folded? What is the connection to parabolas?

Axis of Symmetry- line that divides a parabola into mirror images and passes through the vertex.

Recall that the vertex is the turning point! How do you write the equation of a vertical line?

When asked for the axis of symmetry, ALWAYS write an equation of a line. The equation will be 𝑥=𝒉 The h value is from the vertex form of a parabola 𝑦= 𝑎(𝑥−𝒉) 2 +𝑘

Standard form of a parabola 𝑦=𝒂 𝑥 2 +𝒃𝑥+𝒄 Do you know your ABC’s? a is the coefficient of the 𝑥 2 term b is the coefficient of the x term c is the constant

Do you remember how to change an equation from vertex form to standard form? Instead of working with a, h and k, you will have a, b and c. Make a change!!!!! 𝑦=2 (𝑥+3) 2 +6

What did you notice about a? The axis of symmetry is 𝒙=− 𝒃 𝟐𝒂 You can find the vertex by plugging the x value of the axis of symmetry into the function to find y. Recall the vertex is a turning point (𝒙,𝒚)

How many points do you need to graph a parabola? How can we find them? EASY WAY? Not as easy way?

The y value is either a maximum or minimum at the vertex. When is it a max? When is it a min?

Essential questions What are x and y intercepts? What is the y value of a point that is an x-intercept? How many x intercepts does a parabola have?

Intercept form 𝑦=𝑎(𝑥−𝑝)(𝑥−𝑞) When you plug in 0 for y and solve p and q are the solutions, so p and q are the intercepts.

On the previous graph, how can you find the y-intercept? Any ideas for finding the vertex when you know the x-intercepts?

Don’t forget that you can find domain and range!

Don’t forget you have all kind of goodies in the table on the graphing calculator!

Real life parabolas What does the vertex tell us? What does the max tell us? What do the intercepts tell us?

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Assignment #6 Pg. 61 #5,9,15-20,23,26,33-43,49,61,63