The Quadratic Formula, a guided tour...

The Quadratic Formula

a guided tour...

Goal #1:

I can identify a, b, and c when given a quadratic equation.

Match

What are the values of a, b, and c for the quadratic:

$$x^2+7x+8$$

• a =

• b =

• c =

1

7

8

• 1

• 7

• 8

Match

What are the values of a, b, and c for the quadratic:

$$-x^2-\frac{22}{13}$$

• a =

• b =

• c =

-1

0

-22/13

• -1

• 0

• -22/13

Match

What are the values of a, b, and c for the quadratic:

$$3x^2+\frac{5x}{4}$$

• a =

• b =

• c =

3

5/4

0

• 3

• 5/4

• 0

Match

What are the values of a, b, and c for the quadratic:

$$11\ -\ 2x\ +17x^2$$

• a =

• b =

• c =

17

-2

11

• 17

• -2

• 11

Match

What are the values of a, b, and c for the quadratic:

$$4x^2+\frac{x}{2}+14$$

• a =

• b =

• c =

4

1/2

14

• 4

• 1/2

• 14

Match

What are the values of a, b, and c for the quadratic:

$$-13x^2+8-6x$$

• a =

• b =

• c =

-13

-6

8

• -13

• -6

• 8

Goal #2:

I can substitute a, b, and c into the quadratic formula.

Labeling

Drag and drop the values of a, b, and c into the quadratic formula for:

$$x^2+14x-32$$

tip: values without ( ) go into the formula first, values with ( ) go in second.

Drag labels to their correct position on the image

-32

(1)

1

(14)

14

Labeling

Drag and drop the values of a, b, and c into the quadratic formula for:

$$-2x^2+11x-15$$

tip: values without ( ) go into the formula first, values with ( ) go in second.

Drag labels to their correct position on the image

-2

-11

(-2)

(-11)

-15

Labeling

Drag and drop the values of a, b, and c into the quadratic formula for:

$$27x^2-8$$

tip: values without ( ) go into the formula first, values with ( ) go in second.

Drag labels to their correct position on the image

(0)

-8

(27)

0

27

Labeling

Drag and drop the values of a, b, and c into the quadratic formula for:

$$7x^2-9x+6$$

tip: values without ( ) go into the formula first, values with ( ) go in second.

Drag labels to their correct position on the image

(-9)

(7)

7

6

-9

Goal #3:

I can simplify what is underneath the radical (called the discriminant).

Math Response

Simplify:

$$\sqrt[]{\left(-5\right)^2-4\left(1\right)\left(5\right)}$$

Type answer here

Correct Answer: \sqrt{5}

Deg^°

Rad

Math Response

Simplify:

$$\sqrt[]{\left(6\right)^2-4\left(\frac{1}{2}\right)\left(9\right)}$$

Type answer here

Correct Answer: 3\sqrt{2}

Deg^°

Rad

Math Response

Simplify:

$$\sqrt[]{\left(11\right)^2-4\left(6\right)\left(4\right)}$$

Type answer here

Correct Answer: 5

Deg^°

Rad

Math Response

Simplify:

$$\sqrt[]{\left(-7\right)^2-4\left(5\right)\left(-\frac{5}{2}\right)}$$

Type answer here

Correct Answer: 3\sqrt{11}

Deg^°

Rad

Goal #4:

I can solve for the zeroes of a function using the quadratic formula.

Multiple Choice

Solve using the Quadratic Formula:

$$-3x^2+7x+5$$

• $$x\ =\ \frac{-7\pm\sqrt[]{109}}{-6}$$

• $$x\ =\frac{3\pm i\sqrt[]{131}}{14}$$

• $$x\ =\ \frac{-5\pm\sqrt[]{109}}{-6}$$

Multiple Choice

Solve using the Quadratic Formula:

$$2x^2-14x+20$$

• $$x\ =\ \left\{2,\ 5\right\}$$

• $$x\ =\frac{-2\pm2\ \sqrt[]{281}}{28}$$

• $$x\ =\ -5\pm4\ \sqrt[]{2}$$

Multiple Choice

Solve using the Quadratic Formula:

$$x^2+4x+9$$

• $$x\ =\ \frac{9\pm\sqrt[]{65}}{2}$$

• $$x\ =\frac{-1\pm\sqrt[]{145}}{8}$$

• $$x\ =\ -2\pm i\ \sqrt[]{5}$$