IM2 Final Review: Chapters 3 and 4.

Answer explanation

Foil (x-3)^2.

This means (x-3)(x-3), which will give you x^2-6x+9. Then, combine the 9 and the 10 (from the original equation) to get 19.

Tags

CCSS.MATH.CONTENT.HSF.IF.B.4

Answer explanation

Move the 5 to the other side.

This gives: x^2+8x=-5

Take half of 8, which is 4, square it, which is 16. Add 16 to both sides.

This gives: x^2+8x+16=11

Factor the left side to (x+4)^2, then subtract 11 from both sides.

Tags

CCSS.MATH.CONTENT.HSF.IF.B.4

• (4, -11)

• (-4, -11)

• (4, 53)

• (-4, -43)

Answer explanation

Use the formula: x=-b/2a.

You get -8/2(1) = -4.

Plug in -4 to get -11.

Write as coordinate pair.

Tags

CCSS.MATH.CONTENT.HSF.IF.B.4

• (2,-19)

• (-2, -19)

• (2, 19)

• (-2, 19)

Answer explanation

Change the sign of the number inside the parenthesis, keep the sign of the number behind the parenthesis.

Write as a coordinate pair.

Tags

CCSS.MATH.CONTENT.HSF.IF.B.4

• (3, -32)

• (-3,40)

• (7, -1)

• (-7, 1)

Answer explanation

Change the signs of the numbers inside the parentheses, which gets you 7 and -1. Add them together to get 6, and then divide by 2 to get 3.

Plug in 3 to get y.

Write as a coordinate pair.

Tags

CCSS.MATH.CONTENT.HSF.IF.B.4

What is the equation of the graph shown?

Answer explanation

Change sign of number inside parenthesis, keep the sign of the number behind the parenthesis.

Plot this point, and use -1 as your A-value, which tells us to go right 1 and down 1.

Tags

CCSS.MATH.CONTENT.HSF.IF.B.4

What is the equation of the graph shown?

Answer explanation

Write the equation in vertex form (change x, keep y) and foil out.

Note: There are multiple approaches to this problem.

Use x=-b/2a to find the x value of the equations given, and plug in x to see which one gives the proper vertex.

Tags

CCSS.MATH.CONTENT.HSF.IF.B.4

What is the equation of the graph shown?

Answer explanation

Locate the zeros and change their signs. Plug them in for p and q in the equation f(x)=a(x-p)(x-q). Then look for an a-value that makes the graph make sense (positive a if the graph opens up, negative a if the graph opens down).

Tags

CCSS.MATH.CONTENT.HSF.IF.B.4

Answer explanation

Break 27 into 3x3x3. Remember with square roots, you take 1 out for a PAIR. We have a pair of 3's, so we take out a 3. We also have a left over 3. It stays under the radical.

Then with the variables, we divide the exponent by 2. If it's even, there will be nothing left under the radical. If it's odd, there will be one left under the radical.

Tags

CCSS.MATH.CONTENT.HSN.RN.A.2

Which of the following equations has imaginary solutions?

Answer explanation

Use the discriminant (b^2-4ac). Look for the negative answer. That one has imaginary zeros.

Tags

CCSS.MATH.CONTENT.HSA.REI.A.2