exam 2

Question 1

Section 10.1

Explain the process of extracting square roots.

x^2 = 4

Answer 1

1. Isolate the squared term.
2. Take the square root of each side. (Don’t forget, + and - in front of the constant)
3. Simplify the square root.
4. Solve by isolating the variable.

Question 2

Section 10.1

Explain the process of completing the square.

x^2 + 8x + 20 = 0

(When the diamond/ac process doesn’t work)

Answer 2

1. Write the equation in form: x^2 + bc = c
2. Add the variable from (b/2)^2 to both sides of the equation.
3. Extract the square.
4. Solve the resulting equation.

Don’t forget the + and - for the square root of the constant (right side

Question 3

Section 10.1

What is the shortcut method to completing the square?

(With the “b” variable)

Answer 3

You use the “b/2” to extract the square on the left side and add the result variable of “(b/2)^2” to the right side constant.

EX: (x+3)(x+3) = 2 + 9

Question 4

Section 10.2

What is the quadratic formula?

Answer 4

x = -b + - SQRT b^2 - 4ac / 2a

Question 5

Section 10.2

What is the condition to using the quadratic formula?

(Think of what the equation must be to equal to.)

Answer 5

The equation must be equal to zero.

Question 6

Section 10.3

How can we make an equation that is not a quadratic into a quadratic equation?

(Think substitute)

Answer 6

We substitute “u” for a common variable to make it into a quadratic

Question 7

Section 10.3

When we square both sides of an equation we must always?

Answer 7

Check for extraneous solutions. (Proof/check our solutions)

Question 8

Section 10.3

When solving Rational Equations we must get rid of solutions that produce (blank) in the denominator.

Answer 8

Zero.

Question 9

Section 10.4

The graph of quadratic equations are U-Shaped and called (blank).

Answer 9

Parabolas.

Question 10

Section 10.4

What is the general parent graph of all parabolas?

Answer 10

y = x squared

Question 11

Section 10.4

What is the standard form of (graph) Quadratic Equations?

Answer 11

y = a^2 + bx + c

Question 12

Section 10.4

What are the 4 steps to graphing quadratic equations in the standard form?

Answer 12

1. Finding the vertex
2. Find the y-intercept.
3. Find the x-intercepts (if any).
4. Use axis of symmetry to add any additional points to graph.

Question 13

Section 10.4

How do you find the vertex?

Answer 13

Use the formula x = -b / 2a to find the x-coordinate of the vertex.
Then substitute the x-value in the original equation to find the y-coordinate.

Question 14

Section 10.4

How do you find the y-intercept?

Answer 14

Replace x with 0.

Question 15

Section 10.4

How do you find the x-intercepts (if there are any)?

Answer 15

Replace y with 0 and solve for x (when possible).

Question 16

Section 10.4

What is the axis of symmetry?

Answer 16

A vertical line extending upward from the vertex.

Question 17

Section 10.5

What is the formula to find the area of a triangle?

Answer 17

A = b * h / 2

Question 18

Section 10.5

What is the formula to find the area of a rectangle?

Answer 18

A = L * W

Question 19

Section 10.5

What is the pythagorean theorem formula?

Answer 19

a^2 + b^2 = c^2

Question 20

Section 10.6

When dealing with Quadratic Inequalities (and graphing on a number line) what kind of chart do you need to make?

Answer 20

A test point chart.