Evaluating Quadratic Functions (5.5)

Figuring out values for y given xFiguring out values for x given y

First a little POD

What is the complex conjugate of -6 - 2i?

What is their product?

What is the complex conjugate of m + ni?

What is their product?

For f(x) = 3x2 + 2x -11

Find f(-4).

Find the x-intercepts.

For f(x) = 3x2 + 2x -11

f(-4) = 3(-4)2 + 2(-4) -11 = 29

Find the x-intercepts.

How would we show them in (x, y) form?

3

341

6

3422

6

3442

6

1362

32

)11(3442

11230 2

x

x

x

xx

For f(x) = 3x2 + 2x -11

Find x, if f(x) = 6.

Hint: how do you set this up?

For f(x) = 3x2 + 2x -11

Find x, if f(x) = 6. Set the y side equal to 0, and use the quadratic formula.

Because the discriminant is a non-negative number, we will have real roots.

3

1321

6

1342

6

13162

6

2082

32

)17(3442

01723

112362

2

x

xx

xx

For f(x) = 3x2 + 2x -11

Will f(x) ever equal -5?

Will it ever equal -15?

For f(x) = 3x2 + 2x -11

Will f(x) ever equal -5?

Again, we can tell this is possible because of the discriminant.

6

762

32

)6(3442

0623

1123x52

2

x

xx

x

For f(x) = 3x2 + 2x -11

Will it ever equal -15?

In this case, a negative discriminant tells us that this is not possible– the graph does not reach down to -15.

6

442

32

43442

0423

1123152

2

x

xx

xx

For f(x) = 3x2 + 2x -11

Graph the parabola on your calculators.

Does the parabola ever cross the line y = -5 or the line y = -15?

For f(x) = 3x2 + 2x -11

Graph the parabola on your calculators.

Does the parabola ever cross the line y = -5 or the line y = -15?