Review
Factor 4x^2+12x
4x(x+3)
Every quadratic equation has a U-shaped graph called this.
What is parabola?
Name the vertex of y= (x-3)^2 +4
(3,4)
Graph the equation: y=(x-5)(x-1) . Must include vertex, and at least one additional point on each side.
Vertex (3,-4)
Y-intercept (0,5)
x-intercepts (5,0) & (1,0)
the height h in feet of a small rocket t seconds after it is launched. The path of the rocket is given by the equation: h = -16t^2 + 128t . What is the greatest height the rocket reaches?
What is 256 feet?
Solve (x-2)(x+6)
x=-6
x=2
The highest or lowest point on a parabola.
What is the vertex?
Name the vertex of y= (x+1)^2 - 8
(-1, -8)
Graph the equation: y = (x+2)(x-2) . Must include vertex, and at least one additional point on each side.
Vertex (0,-4)
X-intercepts (2,0) (-2,0)
The height h in feet of a small rocket t seconds after it is launched. The path of the rocket is given by the equation: h = -16t^2 + 128t . Express the interval over which the graph is increasing.
What is from 0 to 4 seconds?
Factor x^2+3x-4
(x+4)(x-1)
When a quadratic equation is written in this form: y = ax^2 +bx + c
What is the standard form?
Name the vertex of y=(x+4)(x-4)
(0,-16)
Graph the equation: y=(x+1)^2 - 2 . Must include vertex, and at least one additional point on each side.
Vertex (-1,-2)
y-intercept (0,-1)
Melissa graphed the equation y = x^2 and Dave graphed the equation y = -3x^ 2 on the same coordinate grid. What is the relationship between the graphs that Melissa and Dave drew?
What is reflected about the x-axis and stretched by a factor of 3?
Factor 3x^2+10x-8
(3x-2)(x+4)
This is the number before the x^2 that determines whether a parabola opens up or down.
What is the leading coefficient?
Name the vertex of
f(x)=x^2 - 4x - 5
(2,-9)
Graph the equation: y=(x-4)^2 + 3 . Must include vertex, and at least one additional point on each side.
Vertex (4,3)
Other points (2,7) and (6,7)
The graph of a parabola is represented by the equation y = ax^2 where a is a positive integer. What happens to the new parabola if a is multiplied by 2?
Stretch by a factor of 2?
Solve x^3-2x^2-25x= -50
x=5, x=-5, x=2
The line that runs through the vertex and divides the parabola in half.
What is axis of symmetry?
Name the vertex of
f(x)=2x^2 + 4x - 6
(-1,-8)
Graph the equation: y=-x^2 -6x + 1 . Must include vertex, and at least one additional point on each side.
Vertex (-3,10)
y-intercept (0,1)
A water balloon is catapulted into the air so that its height h, in meters, after t seconds is h = -4.9t^2 + 27t + 2.4 . What is the maximum height of the balloon rounded to the nearest meter?
What is about 39 meters?