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2.1 Solving Quadratics
2.2 Complex Solutions
2.3 Key Features
2.4 Transformations
100

Solve: 7x2 − 6 = 57

{-3,3}

100

When will a quadratic equation have non-real solutions? Then come up with an example of a non-real solution!

When we are taking the square root of a negative number.

100

Determine the following from the function in Pear Deck:

1) x-intercept(s)

2) y-intercept(s)

3) vertex AND is it a max or min?

4) positive or negative?

5) end behavior?

1) (-2,0) and (0,0)

2) (0,0)

3) (-1,3) ; Max

4) Negative

5) as x → ∞, f(x) → -∞ AND as x → -∞, f(x) → -∞

100

Which part of this function represents a vertical shift and which direction is it moving?

f(x) = -2(x + 3)2 - 8

-8, shifting down

200

Solve: 2k2 + 3k − 14 = 0

{-7/2, 2}

200

Solve: -3k2 - 6 = 21

{-3i,3i}

200

Looking at the function in Pear Deck, determine the average rate of change over the interval [-1,0].

-3

200

Which part of this function represents a horizontal shift and which direction is it moving?

f(x) = -2(x + 3)2 - 8

+3, shifting left

300

Solve: x2 + 5 = -5x

-5/2 +- √5/2

300

Solve: -4(b+3)2 - 2 = 14

-3 +- 2i

300

Determine the following from the function in Pear Deck:

1) Increasing interval:

2) Decreasing interval:

3) Domain:

4) Range:

1) Increasing: (-∞,-1)

2) Decreasing: (-1,∞)

3) (-∞,∞)

4) (-∞,3]

300

What does the -2 tell us about this function in terms of transformations?  (two things!)

f(x) = -2(x + 3)2 - 8

Reflection about the x-axis and a vertical stretch

400

Solve: 2x2 - 14x + 23 = 0

7/2 +- √3/2

400

What value of c will make this quadratic equation produce non-real solutions?

2x2 - 7x + c = 0

Be prepared to explain WHY! (I want an actual number)

Any value greater than or equal to 7 would work!

400

Looking at the graph in Pear Deck, determine the following AND interpret their meaning:

1) Vertex

2) X-intercepts

3) Domain

1) (2,4), there's the largest possible number of mosquitoes (4 million) when rainfall is about 2 cm

2) (0,0) and (4,0), there are no mosquitos when there is no rainfall and when there is 4 cm of rainfall

3) [0,4], rainfall falls between 0 and 4 cm

400

Based on the parabola in Pear Deck, write a new function, g(x), in terms of f that will allow the ball to clear the wall (go over the wall).

g(x) = f(x - 2) + 1