What's the Point?
State the vertex for:
y = -3|x| - 8
V: (0,-8)
State the ordered pair that is the reflection of (0,8) across the axis of symmetry for:
y = |x + 2| + 6
(-4,8)
Given y = -3(x + 5)2 - 8
a) State the vertex
b) State if the vertex is a max or min. Explain.
a) V: (-5,-8)
b) max b/c graph opens down (a is negative)
Factor: 6x2 - 13x - 5
(3x + 1)(2x - 5)
State three other words used to describe "solutions" to a quadratic equation.
x-intercepts
roots
zeros
State the vertex for:
y = 2(x - 7)2 + 4
V: (7,4)
Describe in detail the transformations for
y = 5|x - 2| + 7 when compared
to its parent function y = |x|
shifts 2 units right
narrower by a factor of 5
shifts 7 units up
Given y = -4x2 - 8x + 7
a) state the axis of symmetry
b) state the vertex
a) x = -1
b) V: (-1, 11)
Factor: x2 + 16x + 64
(x + 8)2 or (x + 8)(x + 8)
Describe the 3 possible cases for the solutions of a quadratic equation.
The parabola:
crosses the x-axis twice (2 real roots)
touches the x-axis once (1 real d.r.)
doesn't touch/cross the x-axis (2 complex roots)
State the y-intercept for:
y = 5x2 - 3x - 9
y-int: (0,-9)
Solve: |x + 8| + 2 > 5
x < -11 or x > -5
Describe in detail the transformations for
y = -2/3(x + 4)2 - 9 when compared
to its parent function y = x2
shifts 4 units left
wider by a factor of 2/3
reflects across the x-axis (opens down)
shifts 9 units down
Factor: 4x2 - 9
(2x + 3)(2x - 3)
True or False:
If a quadratic equation cannot be factored then it has no solutions. Explain.
False.
The quadratic formula can be used to solve the quadratic equation.
State the axis of symmetry for:
y = -3x2 + 12x - 4
x = 2
Solve: 2|x - 7| - 6 < -10
no solution b/c |x - 7| < -2
Given the quadratic equation, y = ax2 + bx + c which coefficient can never be equal to zero? Explain?
a can never be equal to zero b/c then x2 would not remain part of the equation
Factor: 2x2 - 3x + 8
prime or not factorable
Solve : 2x2 – 3x = 5
x = 5/2 or 2.5
x = -1