2.1 Solving Quadratics
Solve: 7x2 − 6 = 57
{-3,3}
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.
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) → -∞
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
Solve: 2k2 + 3k − 14 = 0
{-7/2, 2}
Solve: -3k2 - 6 = 21
{-3i,3i}
Looking at the function in Pear Deck, determine the average rate of change over the interval [-1,0].
-3
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
Solve: x2 + 5 = -5x
-5/2 +- √5/2
Solve: -4(b+3)2 - 2 = 14
-3 +- 2i
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]
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
Solve: 2x2 - 14x + 23 = 0
7/2 +- √3/2
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!
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
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