Slides for 2/9 & 2/10 Precalculus. Warm-Up Set 9 Problem 2 Using your calculator, find a line of...

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Slides for 2/9 & 2/10 Precalculus

Transcript of Slides for 2/9 & 2/10 Precalculus. Warm-Up Set 9 Problem 2 Using your calculator, find a line of...

Page 1: Slides for 2/9 & 2/10 Precalculus. Warm-Up Set 9 Problem 2 Using your calculator, find a line of regression for the following data set, and find the correlation.

Slides for 2/9 & 2/10

Precalculus

Page 2: Slides for 2/9 & 2/10 Precalculus. Warm-Up Set 9 Problem 2 Using your calculator, find a line of regression for the following data set, and find the correlation.

Warm-Up Set 9 Problem 2

Using your calculator, find a line of regression for the following data set, and find the correlation coefficient r :

x y

0 6

2 9

4 16

6 18

8 20

10 25

12 31

14 34

Page 3: Slides for 2/9 & 2/10 Precalculus. Warm-Up Set 9 Problem 2 Using your calculator, find a line of regression for the following data set, and find the correlation.

Objectives

Today, we will: Graph a quadratic function by hand using

transformations and using technology. Express a quadratic function in the appropriate form:

Standard form Intercept form Vertex form

Find the intercepts (zeroes) of a quadratic function, and solve quadratic equations.

Page 4: Slides for 2/9 & 2/10 Precalculus. Warm-Up Set 9 Problem 2 Using your calculator, find a line of regression for the following data set, and find the correlation.

Graphing Quadratics

Use your calculator to graph the five example quadratics given here.

How are they alike?

How are they different?

234

1

234

1

23

3

2

2

2

2

2

xxp

xxh

xxg

xxf

xy

Page 5: Slides for 2/9 & 2/10 Precalculus. Warm-Up Set 9 Problem 2 Using your calculator, find a line of regression for the following data set, and find the correlation.

Standard Form for a Quadratic

cbxaxxf 2

In the standard form of a quadratic, the shape of the parabola is controlled by the parameters a, b, and c.

The y-intercept of the parabola is (0, c). If a is positive, the parabola opens upwards; if a is

negative, the parabola opens downwards. The line of symmetry is x = -b/(2a). A quadratic must be in standard form to use the

quadratic formula to find the x-intercepts.

Page 6: Slides for 2/9 & 2/10 Precalculus. Warm-Up Set 9 Problem 2 Using your calculator, find a line of regression for the following data set, and find the correlation.

Intercept Form for a Quadratic qxpxaxf The parameter a in the intercept form does the same thing it

did in the standard form. The x-intercepts of the parabola are (p, 0) and (q, 0) (watch

your signs!). The y-intercept of the parabola is (0, a·p·q). The axis of symmetry is x = (p + q)/2. We factor a quadratic to put it in intercept form – but some

quadratics cannot be factored! A quadratic function with no x-intercepts doesn’t have an intercept form.

Page 7: Slides for 2/9 & 2/10 Precalculus. Warm-Up Set 9 Problem 2 Using your calculator, find a line of regression for the following data set, and find the correlation.

Vertex Form for a Quadratic

khxaxf 2)( Again, a serves the same purpose in the vertex form

as in the two previous forms. The line of symmetry is x = h. The vertex of the parabola is (h, k). The y-intercept of the parabola is (0, a·h² + k). We can find the vertex form from the standard form

by completing the square.

Page 8: Slides for 2/9 & 2/10 Precalculus. Warm-Up Set 9 Problem 2 Using your calculator, find a line of regression for the following data set, and find the correlation.

Finding the Useful Parts When you graph a quadratic function, you must

always list the following important parts: The y-intercept The x-intercepts (if it has them; some parabolas do not) The line of symmetry The vertex

All three forms can give you the y-intercept and the line of symmetry.

To find the x-intercepts, either change to intercept form, or change to standard form and use the quadratic formula.

To find the vertex, either change to vertex form, or plug the x-value of the line of symmetry back into the quadratic function.

Page 9: Slides for 2/9 & 2/10 Precalculus. Warm-Up Set 9 Problem 2 Using your calculator, find a line of regression for the following data set, and find the correlation.

The Quadratic Formula

a

acbbx

2

42

Just in case you forgot, here’s the quadratic formula.

It finds the x-values of the x-intercepts of the parabola.

Since it requires a, b, and c, you have to be in the standard form to use the quadratic formula.